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## Publications

Publications (260)

In the paper, by virtue of an integral representation of the Dirichlet beta function, with the aid of a relation between the Dirichlet beta function and the Euler numbers, and by means of a monotonicity rule for the ratio of two definite integrals with a parameter, the author finds increasing property and logarithmic convexity of two functions and...

In this paper, we present a Tseng-type self-adaptive algorithm for solving a variational inequality and a fixed point problem involving pseudomonotone and pseudocontractive operators in Hilbert spaces. A weak convergent result for such algorithm is proved under a weaker assumption than sequentially weakly continuous imposed on the pseudomonotone op...

In the paper, after concisely surveying some closed formulas and applications of special values of the Bell polynomials of the second kind for some special sequences and elementary functions, the authors newly establish some closed formulas for some special values of the Bell polynomials of the second kind.

The projected subgradient algorithms can be considered as an improvement of the projected algorithms and the subgradient algorithms for the equilibrium problems of the class of monotone and Lipschitz continuous operators. In this paper, we present and analyze an iterative algorithm for finding a common element of the fixed point of pseudocontractiv...

In the paper, the authors present two approximation methods for finding a solution of the split common fixed points problem and obtain weak and strong convergence results.

In this paper, we investigate the monotone variational inequalities and fixed point problems in Hilbert spaces. Two modified extragradient algorithms are presented for finding a common element of the set of fixed points of a pseudocontractive operator and the set of solutions of the variational inequality problem. Weak and strong convergence of the...

In this paper, we propose an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities with a hierarchical fixed point problem constraint for an infinite family of nonexpansive mappings. We show that the proposed algorithms converge strongly to a solution of the general system of variational...

In this paper, the original C Q algorithm, the relaxed C Q algorithm, the gradient projection method ( G P M ) algorithm, and the subgradient projection method ( S P M ) algorithm for the convex split feasibility problem are reviewed, and a renewed S P M algorithm with S-subdifferential functions to solve nonconvex split feasibility problems in fin...

In this paper, we are interested in the pseudomonotone variational inequalities and fixed point problem of pseudocontractive operators in Hilbert spaces. An iterative algorithm has been constructed for finding a common solution of the pseudomonotone variational inequalities and fixed point of pseudocontractive operators. Strong convergence analysis...

Abstract To design a quadratic spline contractual function in the case of discretely unknown nodes, a modified constraint shifting homotopy algorithm for solving principal–agent problems is constructed in the paper. Then the existence of globally convergent solution to KKT systems for the principal–agent problem with spline contractual function is...

In the paper, by the Fàa di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients in two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers.

On the basis of Robinson's normal equation and smoothing projection operator, a homotopy method for solving mathematical programs with box-constrained variational inequalities (MPBVI) is presented. In which, the Chen–Harker–Kanzow–Smale smooth function is used to transform MPBVI into a smooth optimization problem. Under some mild assumptions, the e...

A system of variational inclusions (GSVI) is considered in Banach spaces. An implicit iterative procedure is proposed for solving the GSVI. Strong convergence of the proposed algorithm is given.

In the paper, by methods and techniques in combinatorial analysis and the theory of special functions, the authors discuss two kinds of special values for the Bell polynomials of the second kind for two special sequences, find a relation between these two kinds of special values for the Bell polynomials of the second kind, and derive an identity in...

In the paper, the authors establish some generalized fractional integral inequalities of the Hermite-Hadamard type for (α, m)-convex functions, show that one can find some Riemann-Liouville fractional integral inequalities and classical integral inequalities of the Hermite-Hadamard type, and generalize and extend some known results.

The authors have retracted this article [1] because it significantly overlaps with the previously published article by Zhong and Huang [2]. All authors agree to this retraction.

In this paper, we present two new iterative algorithms for approximating a solution of the multiple-sets split feasibility problem. The suggested algorithms are based on the gradient method with selection technique. Weak and strong convergence theorems are demonstrated.

Multistep composite implicit and explicit extragradient-like schemes are presented for solving the minimization problem with the constraints of variational inclusions and generalized mixed equilibrium problems. Strong convergence results of introduced schemes are given under suitable control conditions.

In this paper, we consider the problem of solving a general system of variational inequalities (GSVI) with a hierarchical variational inequality (HVI) constraint for countably many uniformly Lipschitzian pseudocontractive mappings and an accretive operator in a real Banach space. We propose an implicit composite extragradient-like method based on t...

This paper studies the problems of robust stability and robust stabilization for discrete-time switched periodic systems with time-varying delays and parameter uncertainty. We obtain the novel sufficient conditions to ensure the switched system is robustly asymptotically stable in terms of linear matrix inequalities. To obtain these conditions, we...

The proximal split feasibility problem is investigated in Hilbert spaces. An iterative procedure is introduced for finding the solution of the proximal split feasibility problem. Strong convergence analysis of the presented algorithm is proved.

An extragradient type method for finding the common solutions of two variational inequalities has been proposed. The convergence result of the algorithm is given under mild conditions on the algorithm parameters.

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

This paper is to solve the following variational inequality over the zero point of a maximal monotone operator: Find x * ∈ A ⁻¹ (0) such that 〈(I-T) x *, x-x*〉 ≥ 0 ∀ x ∈ A ⁻¹ (0) where T is a pseudocontractive mapping and A ⁻¹ (0) is the set of zero points of a maximal monotone operator A. An algorithms is presented for solving the above variationa...

The proximal split feasibility problems with two convex and lower semi continuous objective functions are considered. An inertial iterative algorithm is suggested for solving the proximal split feasibility problem. Weak convergence result is given.

In this paper, we introduce and analyze a composite steepest-descent algorithm for solving the triple hierarchical variational inequality problem in a real Hilbert space. Under mild conditions, the strong convergence of the iteration sequences generated by the algorithm is established.

In this paper, we introduce implicit composite three-step Mann iterations for finding a common solution of a general system of variational inequalities, a fixed point problem of a countable family of pseudocontractive mappings and a zero problem of an accretive operator in Banach spaces. Strong convergence of the suggested iterations are given.

In this paper, we study a general system of variational inequalities with a hierarchical variational inequality constraint for an infinite family of nonexpansive mappings. We introduce general implicit and explicit iterative algorithms. We prove the strong convergence of the sequences generated by the proposed iterative algorithms to a solution of...

The purpose of this paper is to solve the general system of variational inclusions (GSVI) with hierarchical variational inequality (HVI) constraint, for an infinite family of continuous pseudocontractive mappings in Banach spaces. By utilizing the equivalence between the GSVI and the fixed point problem, we construct an implicit multiple-viscosity...

The stability for a class of generalized Minty variational-hemivariational inequalities has been considered in reflexive Banach spaces. We demonstrate the equivalent characterizations of the generalized Minty variational-hemivariational inequality. A stability result is presented for the generalized Minty variational-hemivariational inequality with...

The q-Bernoulli numbers and polynomials can be given by Witt’s type formulas as p-adic invariant integrals on Z p . We investigate some properties for them. In addition, we consider two variable q-Bernstein polynomials and operators and derive several properties for these polynomials and operators. Next, we study the evaluation problem for the doub...

In this paper, we study the p-adic integral representation on Zp of q-Bernoulli numbers arising from two variable q-Bernstein polynomials and investigate some properties for the q-Bernoulli numbers. In addition, we give some new identities of q-Bernoulli numbers.

In this paper, we introduce a hybrid viscosity extragradient method for a general system of variational inequalities with solutions being also common fixed points of a countable family of nonexpansive mappings and zeros point of an accretive operator in real smooth Banach spaces. Under quite appropriate assumptions, we obtain some strong convergenc...

In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here the related special numbers are Stirling numbers of the first and second kinds, degenerate Stirling numbers of the first and second kinds, derangement numbers, higher-o...

The purpose of this paper is to exploit umbral calculus in order to derive some properties, recurrence relations, and identities related to the degenerate r-Stirling numbers of the second kind and the degenerate r-Bell polynomials. Especially, we will express the degenerate r-Bell polynomials as linear combinations of many well-known families of sp...

In the framework of real Hilbert spaces, we investigate two viscosity approximation splitting methods for a nonexpansive mapping and two monotone mappings. Two strong convergence theorems are established with the aid of the metric projection. Some applications are also provided to support the main results.

Projection method is used to solve the fixed point problem of firmly type nonexpansive operators. Strong convergence theorem is obtained under the control conditions (CI) and (C2). Our results obtained in this paper give the affirmative answer on the Halpern open problem for this class of operators. As an application, our method can be used to find...

An improved algorithm based on the Korpelevich's method is presented for solving the generalized variational inequality in Banach spaces. Strong convergence results are given under some assumptions.

The split common fixed points problem for demicontractive operators has been considered in Hilbert spaces. An iterative algorithm is constructed. Strong convergence result is given under some mild assumptions. Several corollaries are also included.

The proximal split feasibility problem is considered. An iterative algorithm has been constructed for solving the proximal split feasibility problem. Strong convergence result is given. © 2018 UPB Scientific Bulletin, Series A: Applied Mathematics and Physics. All rights reserved.

The split common fixed points problem for demicontractive operators has been studied in Hilbert spaces. An iterative algorithm is considered and the weak convergence result is given under some mild assumptions.

The split common fixed point problem attempts to find a fixed point of an operator in one space whose image under a linear transformation is a fixed point of another operator in the image space. We formulate and analyze a self-adaptive algorithm for solving this split common fixed point problem for the class of demicontractive operators. Strong con...

The proximal split feasibility problems of two proper and lower semi-continuous convex functions are investigated in Hilbert spaces. An equivalence relation is given. By using this equivalence conclusion, we suggest an iterative algorithm and demonstrate its convergence to a solution of the proximal split feasibility problem.

Mixed equilibrium problems and fixed point problems have been considered. An iterative algorithm with perturbations for finding the common element of mixed equilibrium problems and fixed point problems has been constructed. It is shown that under some mild conditions, the sequence generated by the presented algorithm converges strongly to the commo...

In this paper, we introduce and consider a feedback control system governed by the system of evolution hemivariational inequalities. Several sufficient conditions are formulated by virtue of the properties of multimaps and partial Clarke’s subdifferentials such that the existence result of feasible pairs of the feedback control systems is guarantee...

This paper is devoted to study the existence of solutions for a class of variational-hemivariational-like inequalities in reflexive Banach spaces. Using the notion of the stable (φ, η)-quasimonotonicity, the properties of Clarke’s generalized directional derivative and Clarke’s generalized gradient, we establish some existence results of solutions...

Self-adaptive algorithms are presented for solving the split common fixed point problem of demicontractive operators in Hilbert spaces. Weak and strong convergence theorems are given under some mild assumptions.

The split variational inequality and fixed point problem under nonlinear transformations has been considered. An iterative algorithm is presented to solve this split problem and the strong convergence results are demonstrated.

In this paper, to compute the fixed point of self-mapping on general nonconvex sets with both inequality and equality constraints, the equality constraints are turned into some inequality constraints and a feasible set swelling homotopy is constructed. Under some mild conditions, the existence and global convergence of the smooth homotopy pathways...

A new fixed point method is suggested to solve the split common fixed point problem. By using this fixed point method, we construct an iteration based on Mann's method for solving the split common fixed point problem. Weak convergence theorem is given under some mild assumptions.

This paper is devoted to solve the following monotone variational inequality of finding x∗∈Fix(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^*\in \mathrm{Fix}(T)$...

In this paper, we present an iterative algorithm with hybrid technique for a family of pseudocontractive mappings. It is shown that the suggested algorithm strongly converges to a common fixed point of a family of pseudocontractive mappings.

An iterative algorithm is presented to find the fixed points of a quasi-asymptotic pseudo-contraction in Hilbert spaces. It is shown that the proposed algorithm converges strongly to the fixed point of a quasiasymptotic pseudo-contraction.

A modeling of filtration characteristics during the submerged hollow fiber membrane microfiltration of yeast suspension under aeration condition was developed on the basis of hydrodynamic mathematical equations that describe the local flux distribution, particle deposition and gas-liquid two-phase flow. The effects of average operating flux, fiber...

An iterative algorithm for finding the fixed points of nonexpansive mappings is proposed based on the implicit midpoint rule. Weak convergence of the algorithm is established. As applications, the proposed algorithm is applied to find the solutions of nonlinear time-dependent evolution equations, Fredholm integral equations, variational inequalitie...

An extraordinary split problem, which can be regarded as a superimposition of the split feasibility problem and the split fixed point problem, is considered. A superimposed algorithm is presented. The analysis technique of the suggested algorithm and the corresponding convergence results are demonstrated.
MSC: 47J25, 47H09, 65J15, 90C25.

The purpose of the paper is to construct iterative methods for finding the fixed points of nonexpansive mappings. We present a modified semi-implicit midpoint rule with the viscosity technique. We prove that the suggested method converges strongly to a special fixed point of nonexpansive mappings under some different control conditions. Some applic...

The purpose of the paper is to study the proximal split feasibility problems. For solving the problems, we present new self-adaptive algorithms with the regularization technique. By using these algorithms, we give some strong convergence theorems for the proximal split feasibility problems.

The split common fixed point problem for two quasi-pseudo-contractive operators is studied. Some properties for quasi-pseudo-contractive operators are presented. An iterative algorithm for solving the split common fixed point problem for two quasi-pseudo-contractive operators is constructed. Strong convergence theorems are proved. A unified framewo...

A filtration mathematical model was developed on the basis of complete mass balance and momentum balance for the local flux distribution prediction and optimization of submerged hollow fiber membrane module. In this model, the effect of radial permeate flow on internal flow resistance was considered through a slip parameter obtained from the local...

We introduce an iterative process which converges strongly to a common minimum-norm solution of a variational inequality problem for an-inverse strongly monotone mapping and a fixed point of relatively non-expansive mapping in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of non-lin...

Let C be a nonempty closed convex subset of a real Hilbert space H. Let T: C → C be a Lipschitz pseudocontractive mapping with Fix(T) ≠ 0. In this paper, we first show that as t → 0+, the path x → xt t ∈ (0,1), in C, defined by xt = (1 - β)Pc[(l - t)xt] + βTxt converges strongly to the minimum-norm fixed point of T. Subsequently, by discreting the...

The purpose of this paper is to construct two simple algorithms without involving projection for finding the minimum norm common solution of maximal monotone operators and nonexpansive mappings in Hilbert spaces. Some applications are also included.

The split common fixed points problem associated with the pseudo-contractive mappings is studied. We present an iterative using Ishikawa iterative techniques. Strong convergence analysis is shown.

The split problem, especially the split common fixed point problem, has been studied by many authors. In this paper, we study the split common fixed point problem for the pseudo-contractive mappings and the quasi-nonexpansive mappings. We suggest and analyze an iterative algorithm for solving this split common fixed point problem. A weak convergenc...

In this paper, we introduce two parallel algorithms for finding a zero of the sum of two monotone operators and a fixed point of a nonexpansive mapping in Hilbert spaces and prove some strong convergence theorems of the proposed algorithms. As special cases, we can approach the minimum-norm common element of the zero of the sum of two monotone oper...

The purpose of this paper is to study the split feasibility problem and fixed point problem involved in the pseudocontractive mappings. We construct an iterative algorithm and prove its strong convergence.
MSC: 47J25, 47H09, 65J15, 90C25.

The split common problems for finding the equilibrium points and fixed points have been studied. A parallel superimposed algorithm is introduced to solve this split common problem. Strong convergence theorems are shown with some analysis techniques.
MSC:
49J30, 47H09, 65K10.

In this paper, an implicit net with perturbations for solving the mixed equilibrium problems and fixed point problems has been constructed and it is shown that the proposed net converges strongly to a common solution of the mixed equilibrium problems and fixed point problems. Also, as applications, some corollaries for solving the minimum-norm prob...

Algorithms approach to equilibriumproblems and fixed points problems have been extensively studied in the literature. The purpose of this paper is devoted to consider the minimization problem of finding a point x† with the property where Ω is the intersection of the solution set of equilibrium problem and the fixed points set of nonexpansive mappin...

In this paper, we study the split common fixed point problem, which is to find a fixed point of a quasi-pseudocontractive mapping in one space whose image under a linear transformation is a fixed point of anther quasi-pseudocontractive mapping in the image space. We design and analyze a new iterative algorithm for solving this split common fixed po...

The asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in 1972. Since then, a large number of authors have studied the weak and strong convergence problems of the iterative algorithms for such a class of mappings. It is well known that the asymptotically nonexpansive mappings is a proper subclass of the class of asymptotic...

An iterative algorithm is introduced for the construction of the minimum-norm fixed point of a pseudocontraction on a Hilbert space. The algorithm is proved to be strongly convergent.
MSC:
47H05, 47H10, 47H17.

In this paper, we introduce a modified relaxed projection algorithm and a modified variable-step relaxed projection algorithm for the split feasibility problem in infinite-dimensional Hilbert spaces. The weak convergence theorems under suitable conditions are proved. Finally, some numerical results are presented, which show the advantage of the pro...

In this paper, quasi-variational inclusions and fixed point problems of pseudocontractions are considered. An iterative algorithm is presented. A strong convergence theorem is demonstrated.
MSC:
49J40, 47J20, 47H09, 65J15.

In this paper our aim is to introduce a new class of procedure, the Uniformly Asymptotically Regular-class of procedures (UAR-precedures), showing some examples of procedures as for finite family of mappings, as for infinite family of mappings. Then by a UAR-procedure we prove the convergence of an implicit iterative method and of an explicit itera...

In this paper, we suggest a hybrid method for finding a common element of the set of solution of an equilibrium problem, the set of solution of a pseudomonotone variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The constructed iterative method combines two well-known methods: extragrad...

A Korpelevich-like algorithm has been introduced for solving a generalized variational inequality. It is shown that the presented algorithm converges strongly to a special solution of the generalized variational inequality.
MSC:
47H05, 47J25.

The purpose of this paper is to study the split feasibility problem and the fixed point problem. We suggest a damped algorithm. Convergence theorem is proven.
MSC:
47J25, 47H09, 65J15, 90C25.

The purpose of this paper is to construct two superimposed optimization methods for solving the mixed equilibrium problem and variational inclusion. We show that the proposed superimposed methods converge strongly to a solution of some optimization problem. Note that our methods do not involve any projection.

It is well-known that Mann's algorithm fails to converge for Lipschitzian pseudocontractions. The main purpose of this article is to construct iterative methods for finding the fixed points of pseudocontractive mappings in Hilbert spaces. Strong convergence results are given.

The split feasibility problem and fixed point problem is considered. New algorithm is presented for solving this split problem. Some analytical techniques are demonstrated and strong convergence results are obtained.

Let C be a nonempty closed convex subset of a Hilbert space H , and let T : H → H be a nonlinear mapping. It is well known that the following classical variational inequality has been applied in many areas of applied mathematics, modern physical sciences, computerized tomography and many others. Find a point x ∗ ∈ C such that
〈 T x ∗ , x − x ∗ 〉 ≥...

It is well-known that Mann’s algorithm fails to converge for Lipschitzian pseudocontractions and strong convergence of Ishikawa’s algorithm for Lipschitzian pseudocontractions have not been achieved without compactness assumption on pseudocontractive mapping T or underlying space C. A new algorithm, which couples Ishikawa algorithms with hybrid tec...

In the present paper, an iterative algorithm for solving mixed equilibrium problems and fixed points problems has been constructed. It is shown that under some mild conditions, the sequence generated by the presented algorithm converges strongly to the common solution of mixed equilibrium problems and fixed points problems. As an application, we ca...

Korpelevich’s extragradient method has been studied and extended extensively due to its applicability to the whole class of monotone variational inequalities. In the present paper, we propose a variant extragradient-type method for solving monotone variational inequalities. Convergence analysis of the method is presented under reasonable assumption...

Self-adaptive methods which permit step-sizes being selected self-adaptively are effective methods for solving some important problems, e.g., variational inequality problems. We devote this paper to developing and improving the self-adaptive methods for solving the split feasibility problem. A new improved self-adaptive method is introduced for sol...

An affine algorithm for the split variational inequality and equilibrium problems is presented. Strong convergence result is given.

The projection methods for solving the minimization problems have been extensively considered in many practical problems, for example, the least-square problem. However, the computational difficulty of the projection might seriously affect the efficiency of the method. The purpose of this paper is to construct two algorithms by releasing projection...

The split feasibility problem models inverse problems arising from phase retrieval problems and the intensity modulated radiation therapy. In this paper, two methods have been presented for solving the split feasibility problem. The strong convergence results of presented algorithms have been obtained under some mild conditions. Especially, the min...