Ljubomir Ćirić

University of Belgrade · Faculty of Mechanical Engineering

In this paper, some random common fixed point and coincidence point results are proved with PPF dependence for random operators in separable Banach spaces. Our results present stochastic versions and extensions of recent results of Dhage [J. Nonlinear Sci. Appl. 5 (2012) and Differ. Equ. Appl. 2 (2012)], Kaewcharoen [J. Inequal. Appl. 2013:287] and...

In this paper we introduce new notions of hybrid rational Geraghty and Suzuki-Edelstein type contractive mappings and investigate the existence and uniqueness of PPF dependent fixed point for such mappings in the Razumikhin class, where domain and range of the mappings are not the same. As an application of our PPF dependent fixed point results, we...

In this paper, we introduce the concepts of weakly and partially weakly α-admissible pair of mappings and obtain certain coincidence and fixed point theorems for classes of weakly α-admissible contractive mappings in a b-metric space. As an application, we derive some new coincidence and common fixed point results in a b-metric space endowed with a...

Abbas, Ali and Salvador [Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl. 2013, 2013:243] extended the concept of F− contraction mapping introduced in [21], to two mappings. The aim of this paper is to introduce the notion of a generalized Fg− weak contraction mapping and to study sufficient condition...

http://www.fixedpointtheoryandapplications.com/content/2015/1/78

By using a concept of generalized commuting mappings, we study a new cla.ss pair of mappings. Some fixed point theorems and corresponding example are considered and discussed on such introduced class. The presented results in this work are generalizations and improvements of many important results, in the sense that we are providing more choices of...

Recently, Choudhury et al. proved a coupled coincidence point theorem in a partial order fuzzy metric space. In this paper, we give a new version of the result of Choudhury et al. by removing some restrictions. In our result, the mappings are not required to be compatible, continuous or commutable, and the t-norm is not required to be of Hadžić-typ...

In this paper, we introduce a new concept of probabilistic metric space, which is a generalization of the Menger probabilistic metric space, and we investigate some topological properties of this space and related examples. Also, we prove some fixed point theorems, which are the probabilistic versions of Banach’s contraction principle. Finally, we...

We introduce the concept of triangular αc-admissible mappings (pair of mappings) with respect to ηc nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular αc-admissible mappings (pair of mappings) with respect to ηc nonself-mappings in Razumikhin class. Several...

The existence of fixed points for continuous mappings on general topological spaces via compact subsets is proved. All our results presented here are new and are generalizations, extensions and improvements of the corresponding results due to Ciric, Jungck, Liu and many others. Further, certain results due to Ciric are improved and extended to topo...

In this paper, first we present some coincidence point results for six mappings satisfying the generalized (ψ,ϕ)-weakly contractive condition in the framework of partially ordered Gp-metric spaces. Secondly, we consider α-admissible mappings in the setup of Gp-metric spaces. An example is also provided to support our results.

By taking a counterexample, we prove that the multistep iteration process is faster than the Mann and Ishikawa iteration processes for Zamfirescu operators.

In this paper, we prove several common fixed point theorems for nonlinear mappings with a function ϕ in fuzzy metric spaces. In these fixed point theorems, very simple conditions are imposed on the function ϕ. Our results improve some recent ones in the literature. Finally, an example is presented to illustrate the main result of this paper.

In this article, we introduce the concept of a w-cone distance on topological vector space (tvs)-cone metric spaces and prove various fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces. The techniques of the proof of our theorems are more complex then in the corresponding previously published articles, since a n...

Bhaskar and Lakshimkantham proved the existence of coupled fixed point for a single valued mapping under weak contractive conditions and as an application they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, Lakshmikantham and Ćirić obtained a coupled coin...

Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and be a continuous strictly hemicontractive mapping. Under some conditions, we obtain that the Mann iteration method with error term converges strongly to a unique fixed point of T and is almost T-stable on K. As an application of our results, we establish str...

Recently, in the paper [J. Harjani, B. Lopez and K. Sadarangani; A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space, Abstract and Applied Analysis, Volume (2010), Article ID 190701, 8pages], some fixed point theorems were established for mappings satisfying a rational type cont...

The main purpose of this paper is to establish the convergence, almost common-stability and common-stability of the Ishikawa iteration scheme with error terms in the sense of Xu (J. Math. Anal. Appl. 224:91-101, 1998) for two Lipschitz strictly hemicontractive operators in arbitrary Banach spaces.

We derive some new coupled fixed point theorems for nonlinear contractive maps that satisfied a generalized Mizoguchi-Takahashi's condition in the setting of ordered metric spaces. Presented theorems extends and generalize many well-known results in the literature. As an application, we give an existence and uniqueness theorem for the solution to a...

In this paper, we derive new coincidence and common fixed point theorems for self-maps satisfying a weak contractive condition in an ordered K-metric space. As application, the obtained results are used to prove an existence theorem of solutions of a nonlinear integral equation.

Let C be a convex and compact subset of a space X. In this paper, we consider the following iterative scheme for a one-parameter nonexpansive semigroup {T(t):t≥0} on C: where λ∈(0,1) and {tn}⊂[0,∞), and we prove that, under certain conditions, {xn} converges to a common fixed point of the semigroup {T(t):t≥0}.

In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778–27...

In this paper, we establish coincidence and fixed point theorems for a pair of mappings satisfying a new generalized (ψ,φ)-weak nonlinear contraction type condition in ordered K-metric spaces. The presented results generalize and extend the very recent results of Choudhury and Metiya [B.S. Choudhury and N. Metiya, The point of coincidence and commo...

In this article, a new concept of mixed monotone-generalized contraction in partially ordered probabilistic metric spaces is introduced, and some coupled coincidence and coupled fixed point theorems are proved. The theorems Presented are an extension of many existing results in the literature and include several recent developments. Mathematics Su...

We prove the existence of fuzzy common fixed point of two mappings satisfying a generalized contractive condition in complete ordered spaces. Our results provide extension as well as substantial improvements of several well-known results in the existing literature and initiate the study of fuzzy fixed point theorems in ordered spaces.

We prove some common fixed point theorems in probabilistic semi-metric spaces for families of occasionally weakly compatible mappings. We also give a common fixed point theorem for mappings satisfying an integral-type implicit relation.

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.

We prove some common fixed point theorems in probabilistic semi-metric spaces for families of occasionally weakly compatible mappings. We also give a common fixed point theorem for mappings satisfying an integral-type implicit relation.

We suggest and analyze an iterative algorithm for a finite family of asymptotically nonexpansive mappings. We study the convergence problem of the proposed iterative algorithm for a finite family of asymptotically nonexpansive mappings under some mild conditions in Banach spaces.

Let E be a real reflexive Banach space, which admits a weakly sequentially continuous duality mapping of E into E*, and C be a nonempty closed convex subset of E. Let {T(t):t≥0} be a semigroup of nonexpansive self-mappings on C such that F:=∩t≥0Fix(T(t))≠∅, where Fix(T(t))={x∈C: x=T(t)x}, and let f: C→C be a fixed contractive mapping. If {αn}, {βn}...

In this paper, the concept of a pair of non-linear contraction type mappings in a metric space of hyperbolic type is introduced and the conditions guaranteeing the existence of a common fixed point for such non-linear contractions are established. Presented results generalize and improve some of the known results. An example is constructed to show...

The probabilistic version of the classical Banach Contraction Principle was proved in 1972 by Sehgal and Bharucha-Reid [V.M. Sehgal, A.T. Bharucha-Reid, Fixed points of contraction mappings on PM spaces. Math. Syst. Theory 6, 97–102]. Their fixed point theorem is further generalized by many authors. In the intervening years many others have proved...

We consider w-distance on a complete metric space and prove some common fixed point theorem for commuting maps.

In this note, by providing an example, we prove that the Noor iteration process converges faster then the Mann and Ishikawa iteration processes for Zamfirescu operators.

We introduce partially ordered ℒ-fuzzy metric spaces and prove a common fixed point theorem in these spaces.

In this paper, a concept of monotone generalized contraction in partially ordered probabilistic metric spaces is introduced and some fixed and common fixed point theorems are proved. Presented theorems extend the results in partially ordered metric spaces of Nieto and Rodriguez-Lopez [Contractive mapping theorems in partially ordered sets and appli...

Let (X, ≤) be a partially ordered set and suppose there is a metric d on X such that (X, d) is a complete separable metric space and (Ω, Σ) be a measurable space. In this article a pair of random mappings F: Ω × (X × X) → X and g: Ω × X → X, where F has a mixed g-monotone property on X, and F and g satisfy the non-linear contractive condition (5) b...

The concept of non-self mappings satisfying a new non-linear contractive type condition is introduced, and coincidence and common fixed point theorems in metric spaces of hyperbolic type are proved. Presented theorems generalize and improve recent theorems of Imdad and Kumar [M. Imdad, S. Kumar, Rhoades-type fixed-point theorems for a pair of nonse...

The main purpose of this paper is to introduce a new class of Banach type fuzzy contractions and to present some fixed and common fixed point theorems for these mappings, as well as for the Edelstein fuzzy locally contractive mappings. Two examples are presented to show that our results are genuine generalizations of many known results. Editorial r...

Two concepts of nonlinear contractions for multi-valued mappings in complete metric spaces are introduced and three fixed point theorems are proved. Presented theorems are generalizations of very recent fixed point theorems due to Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces,...

In this paper, new contraction type non-self mappings in a metric space are introduced, and conditions guaranteeing the existence of a common fixed-point for such non-self contractions in a convex metric space are established. These results generalize and improve the recent results of Imdad and Khan [M. Imdad, L. Khan, Some common fixed point theor...

We introduce the concept of a mixed g-monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces. Presented theorems are generalizations of the recent fixed point theorems due to Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham...

In this note, we speed up the convergence of the Picard sequence of iterations for strongly accretive and strongly pseudo-contractive mappings. Our results improve the results of Chidume [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint no. IC2000098; C.E. Chidume, Iterative Algorit...

Let K be a compact convex subset of a real Hilbert space H and T : K -> K a continuous hemi-contractive map. Let {a(n)}, {b(n)} and {c(n)} be real sequences in [0, 1] such that a(n) + b(n) + c(n) = 1, and {u(n)} and {v(n)} be sequences in K. In this paper we prove that, if {b(n)}, {c(n)} and {v(n)} satisfy some appropriate conditions, then for arbi...

In this paper, we introduce the concept of a contractive type non-self mappings for a two pair of multi-valued and single-valued mappings in metric spaces and prove some results on coincidence and common fixed points in complete convex metric spaces. Our theorems generalize and improve the theorems of Imdad and Khan [M. Imdad, L. Khan, Some common...

In this paper the concept of a contraction for multi-valued mappings in a metric space is introduced and the existence theorems for fixed points of such contractions in a complete metric space are proved. Presented results generalize and improve the recent results of Y. Feng, S. Liu [Y. Feng, S. Liu, Fixed point theorems for multi-valued contractiv...

In this paper we introduce and investigate a class of asymptotically nonexpansive mappings which properly extends the class of nonexpansive mappings. We proved general existence theorems for fixed and periodic points of these mappings in arbitrary intuitionistic fuzzy metric spaces and so we solved an open problem, related to periodic points.

In this paper we present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator, defined on a uniformly smooth Banach space. Our study is based on an important result of Reich [S. Reich, An iterative procedure for constructing zeros of ac...

In this paper the existence and approximation of a unique common fixed point of two families of weakly compatible self-maps on a complete metric space are investigated. An example is presented to show that our results for the mappings considered satisfying non-linear contractive type conditions are genuine generalizations of the recent result for m...

For a Lipschitz strongly accretive map considered by Chidume in [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint No. IC2000098; C.E. Chidume, Iterative algorithms for nonexpansive mappings and some of their generalizations, Nonlinear analysis and applications: to V. Lakshmikantam o...

Let (X, d) be a metric spaces of hyperbolic type, C be a closed and of hyperbolic type subset of X and let B(C) be the family of all nonempty bounded subsets of C. In this paper some results on the convergence of the Ishikawa iterates associated with a pair of multi-valued mappings S, T : C → B

Our paper is devoted to the solution of Hilbert's sixth problem, attempting to treat the problem of axiomatization of physics, as well as the foundation of physics as a formal mathematical theory. Within the framework of formal Set Theory, we have built a universe of topological spaces. On such grounds, a formal Space Theory is formulated. A defini...

A concept of g-monotone mapping is introduced, and some fixed and common fixed point theorems for g-non-decreasing generalized nonlinear contractions in partially ordered complete metric spaces are proved. Presented theorems are generalizations of very recent fixed point theorems due to R. P. Agarwal, M. A. El–Gebeily, and D. O’Regan [Appl. Anal. 8...

In this paper, we modify the Ishikawa iteration process and show that such process, associated with a nonlinear Lipschitzian generalized strongly pseudo-contractive operator with a fixed point in a (not necessarily uniformly smooth) Banach space, converges strongly to the unique fixed point of this operator.

Let ( X, d ) be a metric space, k a positive integer and T a mapping of X ^k into X . In this paper we proved that if T satisfies conditions (2.1) and (2.2) below, then there exists a unique x in X such that T ( x, x, ¼ , x ) = x , This result generalizes the corresponding theorems of the second author [4], [5] and the theorem of Dhage...

The existence of coincidence and fixed points for continuous mappings on pseudo-compact completely regular topological spaces are proved. Our results are different from known, or are generalizations, extensions and improvements of the corresponding results due to Jungck, Liu and Liu et al. Further, the Edelstein result for contractive mappings is e...

Abstrac In this paper we obtain some results on coincidence and common fixed points for two pairs of multi-valued and single-valued non-self mappings in complete convex metric spaces. We improve on previously used methods of proof and obtain results for mappings which are not necessarily compatible and not necessarily continuous, generalizing some...

Recently, Pathak [13] has made an extension of the notion of compatibility to weak compatibility, and extended the coincidence theorem for compatible mappings in Kaneko and Sessa [11] to weakly compatible mappings [13]. In the present paper, we define a new class of weakly compatible mappings (Definition 4) and prove some common fixed point theorem...

Let (X,d) be a metric space of hyperbolic type and K a nonempty closed subset of X. In this paper we study a class of mappings from K into X (not necessarily self-mappings on K), which are defined by the contractive condition (2.1) below, and a class of pairs of mappings from K into X which satisfy the condition (2.28) below. We present fixed point...

Jungck's [G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986) 771–779] notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non-self mappings in complete convex metric spaces. We improve on the method of proof used by Rhoades [B.E. Rhoades, A...

Let ( X,d) be a Polish space, CB(X) the family of all nonempty closed and bounded subsets of X, and ( Ω,Σ) a measurable space. A pair of a hybrid measurable mappings f:Ω×X→X and T: Ω×X→CB(X), satisfying the inequality (1.2), are introduced and investigated. It is proved that if X is complete, T(ω,·), f(ω,·) are continuous for all ω∈Ω, T(·,x), f(·,x...

The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let X be a real Banach space and T : D ⊂ X → 2D be a multi-valued operator of generalized monotone type with fixed points. A...

In this paper we prove common fixed-point theorems for a pair of multi-valued non-self-mappings in metrically convex metric spaces. Our results generalize and extend both theorems of Itoh, (Comment. Math. Univ. Carolin. 18 (1977) 247) and Khan, (Pacific J. Math. 95 (1981) 337), the theorem of Assad, (Boll. Un. Math. Ital. 4 (1973) 1), the theorem o...

Two general fixed point theorems for asymptotically regular self-mappings on a metric space X which satisfy the contractive condition (1) below are proved. Our results extend and generalize results of Sharma and Yuel [4] and Guay and Singh [3].

Two general fixed point theorems for asymptotically regular self-mappings on a metric space X which satisfy the contractive condition (1) below are proved. Our results extend and generalize results of Sharma and Yuel [4] and Guay and Singh [3].

In this paper we investigate a class of pairs of Greguš type mapppings I and T on a metric space (X, d) which satisfy the following condition: d(Tx, Ty) ≤ αd(Ix, Iy) + β max{d(Ix, Tx), d(Iy, Ty)} + γmax{d(Ix, Iy), d(Ix, Tx), d(Iy, Ty), b(d(Ix, Ty) + d(Iy, Tx))} for all x, y in X, where α, β, γ are constants such that α > 0, β > 0, γ ≥ 0 and α + β+...

In this paper we introduce and consider a class of multi-valued and single-valued operators of generalised monotone type. We proved a new general lemma on the convergence of real sequences and some new convergence theorems for the Ishikawa and Mann iteration processes with errors to the unique fixed point of such operators, which are not necessaril...

In this paper we consider the strong convergence of the sequence of the Ishikawa iterative process with errors to fixed points and solutions of quasi-strongly accretive and quasi-strongly pseudo-contractive operator equa- tions in Banach spaces. Considered error terms are not necessarily summable. Our main results improve and extend the correspondi...

We prove common fixed point theorems for a pair of multi-valued non-self mappings in metrically convex metric spaces. Our results generalize and extend a theorem of B. E. Rhoades [Commentat. Math. Univ. Carol. 37, No. 2, 401–404 (1996; Zbl 0849.47032)], a theorem of N. A. Assad [Boll. Unione Mat. Ital., IV. Ser. 8, 1–7 (1973; Zbl 0265.54046)] and t...

Let C be a nonempty convex and closed subset of a normed linear space X and CB(C) be a family of all nonempty closed and bounded, not necessarily compact subsets of C. In this paper the convergence of the Ishikawa iterates to a common fixed point of a pair of multivalued mappings S,T: C → CB(C) which satisfy a very general condition (3) below, is c...

Let X be a Banach space, let K be a non–empty closed subset of X and let T : K → X be a non–self mapping. The main result of this paper is that if T satisfies the contractive–type condition (1.1) below and maps ∂K (∂K the boundary of K) into K then T has a unique fixed point in K.

Let X be a normed linear space and let S and T be multi-valued mappings of X into a family of closed, not necessarily compact subsets of X. In this paper some results on the convergence of the Ishikawa iterates associated with a pair S, T which satisfy the condition (8) below, are obtained.

Let (X,d) be a metric space and T:X→X a self-mapping of X. In metric fixed point theory there are many fixed point theorems for contractive-type or expansive-type mappings. In this paper we define a new class of mappings which besides contractive mappings contains some expansive mappings. This class is defined by the following condition: minh d (Tx...

In this paper, we investigate generalized Greguš type mappings. We prove some common fixed point theorems for four mappings, using the concept of weakly biased mappings.

Let C be a convex subset of a complete convex metric space X, and S and T be two selfmappings on C. In this paper it is shown that if the sequence of Ishikawa iterations associated with S and T converges, then its limit point is the common xed point of S and T. This result extends and generalizes the cor-responding results of Naimpally and Singh [6...

In this note we give a correction to the main result of Zhou in [14] on the convergence of the Ishikawa iteration process to a unique fixed point of a strongly pseudocontractive operator in arbitrary real Banach spaces. Our results extend the recent result of Soltuz [11] to arbitrary strongly pseudocontractive operators.

In this paper we prove three common fixed point theorems for a pair of multi-valued non-self mappings in metrically convex metric spaces. Our results generalize and extend several earlier results.

Let C be a closed convex subset of a complete convex metric space X. In this paper a class of selfmappings on C, which satisfy the nonexpansive type condition (2) below, is introduced and investigated. The main result is that such mappings have a unique fixed point.

This paper deals, with the Ishikawa iteration scheme to construct fixed points of nonlinear quasi-contractive mappings in convex metric spaces. The results generalize corresponding results of Chidume (1991) and several other authors.

In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.

In this paper a class of selfmaps on quasi-metric spaces which satisfy the contractive definition (A), or (B), or (C) below are investigated and general common fixed and periodic point theorems are proved. These theorems generalize and extend the fixed point theorem of DOWING and Kirk [7] and a great number of known generalizations of CARISTI's The...

We prove common fixed point theorems for set-valued maps (not necessarily continuous) from complete metric space (X, d) into a class of nonempty closed subsets of X. These theorems include most of the well-known theorems of this type.

In this paper a pair of self-mappings S and T on a complete metric space is considered. We define a nonlinear contraction-type condition (1) below and prove that if S and T satisfy (1) and one of them is continuous, then they have a unique common fixed point.

A wider class of mappings in metric spaces, which have a non-unique fixed point, is introduced and investigated. The presented fixed point theorems include as special cases the corresponding theorems of Dhage, Pachpatte and the first author.

In this note we shall construct a counterexample to the theorem of11.