Kanokwan Sitthithakerngkiet

The Existence and Uniqueness of Coupled Best Proximity Point for Proximally Coupled Contraction in a Complete Ordered Metric Space

We prove the existence and uniqueness of coupled best proximity point for mappings satisfying the proximally coupled contraction in a complete ordered metric space. Further, our result provides an extension of a result due to Bhaskar and Lakshmikantham.

Coupled best proximity points in ordered metric spaces

AbstractIn this paper, we prove the existence and uniqueness of a coupled best proximity point for mappings satisfying the proximally coupled contraction condition in a complete ordered metric space. Further, our result provides an extension of a result due to Luong and Thuan (Comput. Math. Appl. 62(11):4238-4248, 2011; Nonlinear Anal. 74:983-992, 2011). MSC:41A65, 90C30, 47H10.

Modified Hybrid Steepest Method for the Split Feasibility Problem in Image Recovery of Inverse Problems

ABSTRACT In this paper, we regard the CQ algorithm as a fixed point algorithm for averaged mapping, and also try to study the split feasibility problem by the following hybrid steepest method; where {αn}⊂(0,1). It is noted that Xu’s original iterative method can conclude only weak convergence. Consequently, we obtain the sequence {xn} generated by our iteration method converges strongly to , where is the unique solution of the variational inequality Our result extends and improves the result of Xu, as shown in the literature, from weak to strong convergence theorems. Finally, in the last section, numerical examples for study behavior convergence analysis of this algorithm are obtained.

An iterative approximation scheme for solving a split generalized equilibrium, variational inequalities and fixed point problems

ABSTRACT In this paper, we consider a common solution of three problems in Hilbert spaces including the split generalized equilibrium problem, the variational inequality problem and fixed point problem. For finding the solution, we present a new iterative method and prove the strongly convergence theorem under mild conditions. Moreover, some numerical examples are given in the last section.

Proximal Point Algorithm for a Common of Countable Families of Inverse Strongly Accretive Operators and Nonexpansive Mappings with Convergence Analysis

In this paper, we investigate and analyze a proximal point algorithm via viscosity approximation method with error. This algorithm is introduced for finding a common zero point for a countable family of inverse strongly accretive operators and a countable family of nonexpansive mappings in Banach spaces. Our result can be extended to some well known results from a Hilbert space to a uniformly convex and 2−uniformly smooth Banach space. Finally, we establish the strong convergence theorems for the proximal point algorithm. Also, some illustrative numerical examples are presented.

Existence theorems of an extension for generalized strong vector quasi-equilibrium problems

In this paper, we study generalized strong vector quasi-equilibrium problems in topological vector spaces. Using the generalization of Fan-Browder fixed point theorem, we provide existence theorems for an extension of generalized strong vector quasi-equilibrium problems with and without monotonicity. The results in this paper generalize, extend and unify some well-known existence theorems in literature.MSC:49J30, 49J40, 47H10, 47H17.

Convergence analysis of a general iterative algorithm for finding a common solution of split variational inclusion and optimization problems

The purpose of this paper is to introduce a general iterative method for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of split variational inclusion problem in the framework Hilbert spaces. Strong convergence theorem of the sequences generated by the purpose iterative scheme is obtained. In the last section, we present some computational examples to illustrate the assumptions of the proposed algorithms.

Proximal forward-backward splitting method for zeros of sum accretive operators for a fixed point set and inverse problems

In this paper, we investigate regularization method via a proximal point algorithm for solving treating sum of two accretive operators and fixed point problems. Strong convergence theorems are established in the framework of Banach spaces. Also we apply our result to variational inequalities and equilibrium problems. Furthermore, an illustrative numerical example is presented. c ©2017 All rights reserved.