Vasile Berinde

• Universitatea de Nord din Baia Mare

We consider new iterative algorithms for solving split common solution problems in the class of demicontractive mappings. These algorithms are obtained by inserting an averaged term into the algorithms previously used in [He, Z. and Du, W-S., Nonlinear algorithms approach to split common solution problems, Fixed Point Theory Appl. 2012, 2012:130, 1...

This paper analyzes seven substantial distinct classes of contractive-type mappings using the technique of geodesic average perturbation within the framework of CAT(0) spaces. These classes of mappings are shown to be either saturated, in the sense that the geodesic average perturbation technique does not yield any significant new fixed point resul...

We present a heuristic method for finding first integrals for linear and quasi-linear first order partial differential equations, when we are often lead to solve exact ordinary differential equations. The method is inspired by the corresponding one used for integrating first order exact ordinary differential equations of the form $$P(x,y) dx+Q(x,y)...

Using the technique of enriching contractive type mappings, we introduce a more general concept of enriched Ćirić-Reich-Rus contraction than the one studied in [Berinde, V.; Păcurar, M. Fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces. Carpathian J. Math. 37 (2021), no. 2, 173–184.] and provid...

We give some extensions of the beautiful 1968 fixed point theorem of Maia [Maia, M. G. Un’osservazione sulle contrazioni metriche. (Italian) Rend. Sem. Mat. Univ. Padova 40 (1968), 139–143] to three classes of enriched contractive mappings in Banach spaces: enriched contractions, Kannan enriched contractions and Ćirić-Reich-Rus contractions.

The aim of this paper is to show analytically and empirically how ant-based algorithms for medical image edge detection can be enhanced by using an admissible perturbation of demicontractive operators. We thus complement the results reported in a recent paper by the second author and her collaborators, where they used admissible perturbations of de...

Our aim in this paper is to study the asymptotic global stability of the positive solutions for a class of first-order nonlinear difference equations with a remarkable feature: the initial conditions are intrinsic and not explicitly given. Global stability results are obtained in a particular case and then for a general class of first-order differe...

In this paper, we construct a novel algorithm for solving non-smooth composite optimization problems. By using inertial technique, we propose a modified proximal gradient algorithm with outer perturbations, and under standard mild conditions, we obtain strong convergence results for finding a solution of composite optimization problem. Based on bou...

Following a well established tradition of marking the main anniversary moments of the journal by an editorial, see the previous ones: [Berinde, V., Anniversary: Ten years of publication of the new series of Buletin S¸ tiint¸ific, Bul. S¸ tiint¸. Univ. Baia Mare, Ser. B., Matematica-Informatic ˘ a,˘ 16 (2000), No. 1, i–ii], [Berinde, V., Carpathian...

We introduce a large class of contractive mappings, called enriched contractions, a class which includes, amongst many other contractive type mappings, the Picard–Banach contractions and some nonexpansive mappings. We show that any enriched contraction has a unique fixed point and that this fixed point can be approximated by means of an appropriate...

In this paper, we prove convergence theorems for a fixed point iterative algorithm of Krasnoselskij-Mann typeassociated to the class of enriched nonexpansive mappings in Banach spaces. The results are direct generaliza-tions of the corresponding ones in [Berinde, V.,Approximating fixed points of enriched nonexpansive mappings byKrasnoselskij iterat...

Let (M,d) be a metric space. In this paper we survey some of the most relevant results which relate the three concepts involved in the title: a) the asymptotic regularity; b) the existence (and uniqueness) of fixed points and c) the convergence of the sequence of successive approximations to the fixed point(s), for a given operator f : M ? M or for...

In this paper, we study the split common fixed point problem in Hilbert spaces. We find a common solution of the split common fixed point problem for two demicontractive operators without a priori knowledge of operator norms. A strong convergence theorem is obtained under some additional conditions and numerical examples are included to illustrate...

Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, presented here for the first time, we introduce and study the class of {\it enriched nonexpansive mappings} in Hilbert spaces. In order to approximate the fixed points of enriched nonexpansive mappings we use the Krasnoselskij iteration for which we prove str...

The aim of this paper in to introduce a large class of mappings, called {\it enriched Kannan mappings}, that includes all Kannan mappings and some nonexpansive mappings. We study the set of fixed points and prove a convergence theorem for Kransnoselskij iteration used to approximate fixed points of enriched Kannan mappings in Banach spaces. We then...

We introduce a large class of mappings, called enriched contractions, which includes, amongst many other contractive type mappings, the Picard-Banach contractions and some nonexpansive mappings. We show that any enriched contraction has a unique fixed point and that this fixed point can be approximated by means of an appropriate Kransnoselskij iter...

In this paper, we introduce and study the class of {\it enriched strictly pseudocontractive mappings} in Hilbert spaces and extend the corresponding convergence theorem (Theorem 12) in [Browder, F. E., Petryshyn, W. V., {\it Construction of fixed points of nonlinear mappings in Hilbert space}, J. Math. Anal. Appl. {\bf 20} (1967), 197--228] and The...

Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, introduced in [Berinde, V., {\it Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces}, Carpathian J. Math. {\bf 35} (2019), no. 3, 277-288.], we introduce the class of enriched Chatterjea contractions and...

In this paper we are concerned with the computation of the antiderivatives on R of a special class of continuous periodic functions. Finally, some applications of the main result are presented.

In this paper, we consider the existence theorem of coincidence point for a pair of single-valued and multi-valued mapping that are concerned with the concepts of cyclic contraction type mapping. Some illustrative examples and remarks are also discussed.

We introduce Prešić-Kannan nonexpansive mappings on the product spaces and show that they have a unique fixed point in uniformly convex metric spaces. Moreover, we approximate this fixed point by Mann iterations. Our results are new in the literature and are valid in Hilbert spaces, CAT(0) spaces and Banach spaces simultaneously.

Some fixed point theorems for discontinuous mappings in Banach spaces by Berinde and Păcurar [Fixed point theorems for non-self single-valued almost contractions, Fixed Point Theory 14 (2013), 301-311] and Kirk [Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math. 17 (1974), 339-346] are extended t...

A general convergence theorem for the Ishikawa fixed point iteration procedure in a large class of quasi-contractive type operators is given. As particular cases, it contains convergence theorems for Picard, Krasnoselskij and Mann iterations, theorems which extend and generalize several results in the literature.

In this paper we give a report on the international impact and visibility of the articles published in the prestigious Romanian monthly Gazeta Matematic\u a during more than 121 years of existence (1895-present). The report is mainly based on those articles that were indexed in one, two or more of the following four databases: Zentralblatt MATH, Ma...

In this paper we obtain general coupled and triple fixed point theorems for mixed monotone almost contractive operators by considering a more general contractive condition and thus extending several previous results in literature.

Let (X, d) be a metric space, Y ⊂ X a nonempty closed subset of X and let f: Y → X be a non self operator. In this paper we study the following problem: under which conditions on f we have all of the following assertions: 1. The operator f has a unique fixed point; 2. The operator f satisfies a retraction-displacement condition; 3. The fixed point...

The aim of this chapter is to survey the most relevant developments done in the last decade around the concept of almost contraction, introduced in Berinde V, Approximating fixed points of weak contractions using the Picard iteration. iteration. Nonlinear Anal. Forum 2004;9(1):43–53.

Starting from the classical Caristi fixed point theorem and its various versions, the aim of this chapter is to study Caristi-Browder operators in the following settings: (1) metric spaces; (2) ℝ+m-metric spaces; (3) s(ℝ+)-metric spaces; (4) Kasahara spaces. Some new research directions in the Caristi-Browder operator theory are also indicated.

Two open problems in the fixed point theory of quasi metric spaces posed in [Berinde, V. and Choban, M. M., {\it Generalized distances and their associate metrics. Impact on fixed point theory}, Creat. Math. Inform. {\bf 22} (2013), no. 1, 23--32] are considered. We give a complete answer to the first problem, a partial answer to the second one, an...

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion from [A. Roldan, J. Martinez-Moreno, C. Roldan, {\it Multidimensional fixed point theorems in partially ordered c...

We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [Choban, M., Berinde, V., {\it A general concept of multiple f...

Two open problems in the fixed point theory of quasi metric spaces posed in [Berinde, V. and Choban, M. M., {\it Generalized distances and their associate metrics. Impact on fixed point theory}, Creat. Math. Inform. {\bf 22} (2013), no. 1, 23--32] are considered. We give a complete answer to the first problem, a partial answer to the second one, an...

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion from [A. Roldan, J. Martinez-Moreno, C. Roldan, {\it Multidimensional fixed point theorems in partially ordered c...

We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [Choban, M., Berinde, V., {\it A general concept of multiple f...

We obtain a fixed point theorem for Prešić nonexpansive mappings on the product of CAT (0) spaces and approximate this fixed points through Ishikawa type iterative algorithms under relaxed conditions on the control parameters. Our results are new in the literature and are valid in uniformly convex Banach spaces.

In a recent paper [H.K. Pathak, R.P. Agarwal, Y.J. Cho, Coincidence and fixed points for multi-valued mappings and its application to nonconvex integral inclusions, J. Comput. Appl. Math. 283 (2015) 201–217.], the authors have studied some problems on coincidence points and fixed points of multi-valued mappings. In order to illustrate the generalit...

"In order to mark the 25th anniversary of the journal Creative Mathematics and Informatics, we give a brief account on the main facts on its evolution since the previous anniversary notice published 5 years ago [Berinde, V., Creative Mathematics and Informatics: Celebrating 20 years of publication, Creat. Math. Inform., 20 (2011), No. 2, i – vi]. o...

Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges....

Let (X, d) be a complete metric space and f: X → X be an operator with a nonempty fixed point set, i.e., \(F_{f}:=\{ x \in X: x = f(x)\}\neq \emptyset\). We consider an iterative algorithm with the following properties: (1) for each x ∈ X there exists a convergent sequence (x n (x)) such that \(x_{n}(x) \rightarrow x^{{\ast}}(x) \in F_{f}\) as \(n...

Let K be a non-empty closed subset of a Banach space X endowed with a graph G. We obtain fixed point theorems for nonself G-contractions of Chatterjea type. Our new results complement and extend recent related results [Berinde, V., Păcurar, M., The contraction principle for nonself mappings on Banach spaces endowed with a graph, J. Nonlinear Convex...

There exist many papers written in the last 50 years or so which are using a concept of rapidity of convergence for two comparable sequences. It appears that the original source of this notion is not known to most of the authors of those papers, since for this notion they are refereeing to different sources or simply do not refer to any other publi...

We introduce modified Noor iterative method in a convex metric space and apply it to approximate fixed points of quasi-contractive operators introduced by Berinde [6]. Our results generalize and improve upon, among others, the corresponding results of Berinde [6], Bosede [9] and Phuengrattana and Suantai [20]. We also compare the rate of convergenc...

Let K be a non-empty closed subset of a Banach space X endowed with a graph G. The main result of this paper is a fixed point theorem for nonself Kannan G-contractions T: K → X that satisfy Rothe’s boundary condition, i.e., T maps ∂K (the boundary of K) into K. Our new results are extensions of recent fixed point theorems for self mappings on metri...

Let X be a Banach space, A and B two non-empty closed subsets of X and let T: A ⋃ B → X be an operator. We define the notion of cyclic non-self almost contraction and we give a corresponding fixed point theorem.

In this paper we establish the existence and uniqueness of a coupled fixed point for operators F: X×X → X satisfying a new type of contractive condition, which is weaker than all the corresponding ones studied in literature so far. We also provide constructive features to our coupled fixed point results by proving that the unique coupled fixed poin...

This year, Carpathian Journal of Mathematics (CJM) reaches an important milestone -25 years of publication of its new series. Following an already well established tradition of marking the main anniversary moments of the journal by an editorial, see [Berinde, V., Anniversary: Ten years of publication of the new series of Buletin Stiintific, Bul. St...

In this paper we establish the existence and uniqueness of a coupled fixed point for operators F: X×X → X satisfying a new type of contractive condition, which is weaker than all the corresponding ones studied in literature so far. We also provide constructive features to our coupled fixed point results by proving that the unique coupled fixed poin...

Starting from the papers [Berinde, V., Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 4889-4897], [ Borcut, M., Berinde, V., Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput., 218 (10) (2012), 5929...

V. Istrat¸escu [Istr ˘ at¸escu, V. I., ˘ On a functional equation, J. Math. Anal. Appl., 56 (1976), No. 1, 133–136] used the Banach contraction mapping principle to establish an existence and approximation result for the solution of the functional equation ϕ(x) = xϕ((1 − α)x + α) + (1 − x)ϕ((1 − β)x), x ∈ [0, 1], (0 < α ≤ β < 1), which is important...

In a previous paper by the third author (IARus, An abstract point of view..., Fixed point Theory 13 (2012), 179-192), a new approach to fixed point iterative methods, based on the concept of admissible perturbation of a self operator, has been established. In continuation of that study, in the present paper we are concerned with the same problem bu...

We establish convergence of a Krasnoselskij type fixed point iterative method constructed as the admissible perturbation of a nonlinear Lipschitzian and generalized pseudocontractive operator defined on a convex closed subset of a Hilbert space. Both a prioxi and a posteriori error estimates are obtained for the new algorithm. Our convergence theor...

Let K be a non-empty closed subset of a Banach space X endowed with a graph G and let T: K → X be a G-contraction that satisfies Rothe's boundary condition, i.e., T maps ∂K (the boundary of K) into K. The main results obtained in this paper are fixed point theorems for nonself G-contractions on a Banach space endowed with a graph. Our new results a...

Let X be a Banach space, A and B two non-empty closed subsets of X and let T: A ⋃ B → X be an operator. We define the notion of cyclic non-self almost contraction and we give a corresponding fixed point theorem.

Two lemmas concerning the superior bound of a numerical sequence satisfying a common recurrence inequality are given. As applications, the error estimations are obtained for the Picard and Mann iterations in the case of demicontractive mappings. Additional conditions that ensure the strong convergence in the same cases can be obtained on the basis...

We introduce the concept of stability of a k-step fixed point iterative method xn+1=T(xn,xn−1,…,xn−k+1), n≥k−1, and study the stability of this equation for mappings T:Xk→X satisfying some Prešić type contraction conditions. Our results naturally extend various stability results of fixed point iterative methods in literature, from contractive self-...

The main aim of this note is to present some data about the education, professional activity and scientific publications of Professor Eugen Grebenikov (1932-2013), a distinguished mathematician born in 1932 at Slobozia Mare, Ismail county, Romania (now in Republic of Moldova) who was educated and had worked for most of his life time in Moscow. Some...

We present new results on the existence and uniqueness of tripled fixed points for nonlinear mappings in partially ordered complete metric spaces that extend the results in the previous works: Berinde and Borcut, 2011, Borcut and Berinde, 2012, and Borcut, 2012. An example and an application to support our new results are also included in the paper...

We prove weak and strong convergence theorems for a double Krasnoselskij-type iterative method to approximate coupled solutions of a bivariate nonexpansive operator [InlineEquation not available: see fulltext.], where C is a nonempty closed and convex subset of a Hilbert space. The new convergence theorems generalize, extend, improve, and complemen...

Let X be a convex metric space, K a non-empty closed subset of X and T: K → X a non-self almost contraction. Berinde and Pǎcurar [Berinde, V. and Pǎcurar, M., Fixed point theorems for nonself single-valued almost contractions, Fixed Point Theory, 14 (2013), No. 2, 301-312], proved that if T has the so called property (M) and satisfies Rothe's bound...

We prove some convergence theorems for a Krasnoselskij type fixed point iterative method constructed as the admissible perturbation of a nonlinear φ-pseudocontractive operator defined on a convex and closed subset of a Hilbert space. These new results extend and unify several related results in the current literature established for contractions, s...

Let (X, d) be a complete metric space and let f : X -> X be a self operator. In this paper we study the following two problems: Problem 1. Let f be such that its fixed points set is a singleton, i.e., F-f = {x*}. Under which conditions the next implication does hold: f is asymptotically regular double right arrow f is a Picard operator? Problem 2....

The main aim of this note is to highlight the role of the Pompeiu-Hausdorff metric in fixed point theory and, subsidiarily, to touch some issues related to the history of this fundamental concept in modern mathematics. This will allow us to conclude that what is nowadays almost generally called Hausdorff metric (distance) and very seldom Hausdorff-...

We consider multivalued nonself-weak contractions on convex metric spaces and establish the existence of a fixed point of such mappings. Presented theorem generalizes results of M. Berinde and V. Berinde (2007), Assad and Kirk (1972), and many others existing in the literature.

Let X be a Banach space, K a non-empty closed subset of X and let T: K -> X be a non-self almost contraction. The main result of this paper shows. that if T has the so called property (M) and satisfies Rothe's boundary condition, i.e., maps partial derivative K (the boundary of K) into K, then T has a fixed point in K. This theorem generalizes seve...

In the last years there has appeared an abundance of fixed point theorems in the literature, most of them established in various generalized metric spaces. Amongst the generalized spaces considered in those papers, we may find: cone metric spaces, quasimetric spaces (or b-metric spaces), partial metric spaces, G-metric spaces etc. In some recent pa...

The aim of this paper is to prove some convergence theorems for a general fixed point iterative method defined by means of the new concept of admissible perturbation of a nonlinear operator, introduced by I. A. Rus [Fixed Point Theory 13, No. 1, 179–192 (2012; Zbl 06200653)]. The obtained convergence theorems extend and unify some fundamental resul...

The aim of this paper is to establish new sequences which converge towards the Euler-Mascheroni constant. Our results solve some open problems posed by V. Berinde [Creat. Math. Inform. 18, No. 2, 123–128 (2009; Zbl 1265.40002)] and extend some results of D. W. DeTemple [Am. Math. Mon. 100, No. 5, 468–470 (1993; Zbl 0858.11068)] and A. Sîntămărian [...

We prove a coupled coincidence point theorem in partially ordered metric spaces for mappings F : X×X = X having the g-mixed monotone property. The main result of this paper extends and improves the corresponding results in [6][10][8][4]. Some examples are given to illustrate our work.

This paper describes the main aspects of the “piecewise-linear homotopy method” for fixed point approximation proposed by C. B. Eaves and R. Saigal [Math. Program. 3, 225–237 (1972; Zbl 0258.65060)]. The implementation of the method is developed using the modern programming language C# and then is used for solving some unconstrained optimization pr...

In this paper, following [W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79-89], we give a fixed point result for cyclic weak (psi, C)-contractions on partial metric space. A Maia type fixed point theorem for cyclic weak (psi, C)-contractions is also gi...

In the present paper we prove some fixed point theorems for Ćirić-type strong almost contractions on partial metric spaces. We also give an illustrative example.

We obtain coupled coincidence and coupled common fixed point theorems for mixed gg-monotone nonlinear operators F:X×X→XF:X×X→X in partially ordered metric spaces. Our results are generalizations of recent coincidence point theorems due to Lakshmikantham and Ćirić [V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions...

In this article we obtain, in the setting of metric spaces or ordered metric spaces, coincidence point, and common fixed point theorems for self-mappings in a general class of contractions defined by an implicit relation. Our results unify, extend, generalize many related common fixed point theorems from the literature. Mathematics Subject Classif...

In this paper, we establish tripled coincidence point theorems for a pair of mappings F : X x X x X -> X and g : X -> X satisfying a nonlinear contractive condition ordered metric spaces. Presented theorems extend reveral existing results in the literature: [V. Lakshmikantham, L. Ciric, Coupled fixed point theorems for nonlinear contractions in par...

In this paper we obtain constructive fixed point theorems for self op-erators in a general class of almost contractions defined by an implicit relation. Our results unify, extend, generalize, enrich and complement a multitude of related fixed point theorems from the literature.

The notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhaskar and Lakshmikantham in [11] investigated the coupled fixed points in the setting of partially ordered set by defining the notion of mixed monotone property. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut [7]. Fo...

The aim of this note is to obtain a generalization of a very simple, elegant but powerful convergence lemma introduced by C. Mortici [Appl. Math. Comput. 215, No. 11, 4044–4048 (2010; Zbl 1186.33003); Am. Math. Mon. 117, No. 5, 434–441 (2010; Zbl 1214.40002); Arch. Math. 93, No. 1, 37–45 (2009; Zbl 1186.40004); Carpathian J. Math. 25, No. 2, 186–19...

In this paper we use Wynn’s ϵ-algorithm to accelerate certain numerical sequences, in order to study empirically their rate of convergence, for the sequence of successive approximations associated with some test functions and ordinary differential equations. For the great majority of the test sequences, the ϵ-algorithm does not improve the converge...

In this paper, we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence, and existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent coupled fixed point theorems established by Gnana Bhaskar and Lakshmikantham [T. Gnana B...

We obtain existence results regarding the solutions g of a Steinhaus type functional equation of the form g(x)+g(f(x))=F(x), under the significantly weaker assumption that f is a weakly Picard operator. The solutions are given in terms of sums of either convergent series or divergent series but summable by some method of summability.

In this paper we extend the coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ obtained in [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. TMA \textbf{65} (2006) 1379-1393] by significantly weakening the involved contractive cond...

In this paper we extend the coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ obtained in [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. \textbf{65} (2006) 1379-1393] and [N.V. Luong and N.X. Thuan, \textit{Coupled fixed points...

We obtain coupled coincidence and coupled common fixed point theorems for mixed $g$-monotone nonlinear operators $F:X \times X \rightarrow X$ in partially ordered metric spaces. Our results are generalizations of recent coincidence point theorems due to Lakshmikantham and \' Ciri\' c [Lakshmikantham, V., \' Ciri\' c, L., \textit{Coupled fixed point...

In this paper we introduce generalized symmetric Meir-Keeler contractions and prove some coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ in partially ordered metric spaces. The obtained results extend, complement and unify some recent coupled fixed point theorems due to Samet [B. Samet, \textit{Coupled fixed p...

In order to mark the 20th anniversary of the journal which currently holds the name Creative Mathematics and Informatics, this note gives a brief account on the main chronological points and present some data to illustrate the evolution of its editorial policy and profile in the period 1991-2011.

In this paper, by using the technique of non expansive operators we shall establish sufficient conditions for the existence of solutions for a class of boundary value problems for fractional differential equations involving the Caputo fractional derivative and nonlinear integral boundary value conditions.

We obtain new and very general stability results for Picard iteration associated to self operators satisfying an implicit relation. Our stability results unify, extend, generalize, enrich and complement a multitude of related stability results from recent literature.

We introduce and illustrate by suitable examples the use of a unified fixed point method for studying the convergence of nonlinear recurrence sequences and for solving cyclic nonlinear systems of equations. Our technique is essentially based on some Presic type fixed point theorems.

The existence of common fixed points is established for three mappings where T is either generalized (f, g)-nonexpansive or asymptotically (f, g)-nonexpansive on a set of fixed points which is not necessarily starshaped. As applications, the invariant best simultaneous approximation results are proved.

We prove the existence of coincidence points and common fixed points for a large class of almost contractions in cone metric spaces. These results generalize, extend and unify several well-known recent related results in literature.

In this note we discuss two subspace completeness conditions involved in some recent common fixed point theorems, show that they are indeed weaker than the completeness assumption of the whole ambient space and find a unifying condition for both. Using this fact, several common fixed point theorems are then reformulated under slightly more general...

Existence theorems for some iterative differential equations as well as convergence theorems for a fixed point iterative method designed to approximate these solutions, are proved under weaker conditions than those due to A. Buic˘ a ("Existence and continuous dependence of solutions of some functional-differential equations," Seminar on Fixed Point...

The purpose of this paper is to study the problem of weak stability of common fixed point iterative procedures for some classes of contractive type mappings. An example to illustrate weakly stable but not stable iterative fixed point procedures is also given.

We prove the existence of coincidence points and common fixed points of noncommuting almost contractions in metric spaces. Moreover, a method for approximating the coincidence points or the common fixed points is also constructed, for which both a priori and a posteriori error estimates are obtained. These results generalize, extend and unify sever...