oalib

Publish in OALib Journal

ISSN: 2333-9721

APC: Only $99

Submit

Search Results: 1 - 10 of 56 matches for " Prasit Cholamjiak "
All listed articles are free for downloading (OA Articles)
Page 1 /56
Display every page Item
On Ishikawa-type iteration with errors for a continuous real function on an arbitrary interval
Prasit Cholamjiak
Applied Mathematical Sciences , 2013,
Abstract: We consider the Ishikawa-type iteration process with errors for acontinuous real function on an arbitrary interval and prove the convergencetheorem. Furthermore, we give numerical examples to comparewith Mann and Ishikawa iteration processes with error sequences.
A projection method for relatively nonexpansive mappings in Banach spaces
Prasit Cholamjiak
Applied Mathematical Sciences , 2013,
Abstract: We introduce a new projection algorithm for solving the fixed pointproblem of relatively nonexpansive mappings in the framework of Banachspaces. We also prove the strong convergence theorem for suchmappings.
A Hybrid Iterative Scheme for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Banach Spaces
Cholamjiak Prasit
Fixed Point Theory and Applications , 2009,
Abstract: The purpose of this paper is to introduce a new hybrid projection algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of the variational inequality for an inverse-strongly monotone operator and the set of fixed points of relatively quasi-nonexpansive mappings in a Banach space. Then we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space.
A Hybrid Iterative Scheme for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Banach Spaces
Prasit Cholamjiak
Fixed Point Theory and Applications , 2009, DOI: 10.1155/2009/719360
Abstract: The purpose of this paper is to introduce a new hybrid projection algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of the variational inequality for an inverse-strongly monotone operator and the set of fixed points of relatively quasi-nonexpansive mappings in a Banach space. Then we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space.
Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces
Prasit Cholamjiak,Suthep Suantai
Abstract and Applied Analysis , 2010, DOI: 10.1155/2010/141376
Abstract: We introduce a new hybrid iterative scheme for finding a common element in the solutions set of a system of equilibrium problems and the common fixed points set of an infinitely countable family of relatively quasi-nonexpansive mappings in the framework of Banach spaces. We prove the strong convergence theorem by the shrinking projection method. In addition, the results obtained in this paper can be applied to a system of variational inequality problems and to a system of convex minimization problems in a Banach space. 1. Introduction Let be a real Banach space, and let be the dual of . Let be a closed and convex subset of . Let be bifunctions from to , where is the set of real numbers and is an arbitrary index set. The system of equilibrium problems is to find such that If is a singleton, then problem (1.1) reduces to find such that The set of solutions of the equilibrium problem (1.2) is denoted by . Combettes and Hirstoaga [1] introduced an iterative scheme for finding a common element in the solutions set of problem (1.1) in a Hilbert space and obtained a weak convergence theorem. In 2004, Matsushita and Takahashi [2] introduced the following algorithm for a relatively nonexpansive mapping in a Banach space : for any initial point , define the sequence by where is the duality mapping on , is the generalized projection from onto , and is a sequence in . They proved that the sequence converges weakly to fixed point of under some suitable conditions on . In 2008, Takahashi and Zembayashi [3] introduced the following iterative scheme which is called the shrinking projection method for a relatively nonexpansive mapping and an equilibrium problem in a Banach space : They proved that the sequence converges strongly to under some appropriate conditions. 2. Preliminaries and Lemmas Let be a real Banach space, and let be the unit sphere of . A Banach space is said to be strictly convex if, for any , It is also said to be uniformly convex if, for each , there exists such that, for any , It is known that a uniformly convex Banach space is reflexive and strictly convex. The function which is called the modulus of convexity of is defined as follows: The space is uniformly convex if and only if for all . A Banach space is said to be smooth if the limit exists for all . It is also said to be uniformly smooth if the limit (2.4) is attained uniformly for . The duality mapping is defined by for all . If is a Hilbert space, then , where is the identity operator. It is also known that, if is uniformly smooth, then is uniformly norm-to-norm continuous on bounded subset
A New Hybrid Algorithm for Variational Inclusions, Generalized Equilibrium Problems, and a Finite Family of Quasi-Nonexpansive Mappings
Prasit Cholamjiak,Suthep Suantai
Fixed Point Theory and Applications , 2009, DOI: 10.1155/2009/350979
Abstract: We proposed in this paper a new iterative scheme for finding common elements of the set of fixed points of a finite family of quasi-nonexpansive mappings, the set of solutions of variational inclusion, and the set of solutions of generalized equilibrium problems. Some strong convergence results were derived by using the concept of W-mappings for a finite family of quasi-nonexpansive mappings. Strong convergence results are derived under suitable conditions in Hilbert spaces.
A New Hybrid Algorithm for Variational Inclusions, Generalized Equilibrium Problems, and a Finite Family of Quasi-Nonexpansive Mappings
Cholamjiak Prasit,Suantai Suthep
Fixed Point Theory and Applications , 2009,
Abstract: We proposed in this paper a new iterative scheme for finding common elements of the set of fixed points of a finite family of quasi-nonexpansive mappings, the set of solutions of variational inclusion, and the set of solutions of generalized equilibrium problems. Some strong convergence results were derived by using the concept of -mappings for a finite family of quasi-nonexpansive mappings. Strong convergence results are derived under suitable conditions in Hilbert spaces.
Weak Convergence Theorems for a Countable Family of Strict Pseudocontractions in Banach Spaces
Prasit Cholamjiak,Suthep Suantai
Fixed Point Theory and Applications , 2010, DOI: 10.1155/2010/632137
Abstract:
Weak Convergence Theorems for a Countable Family of Strict Pseudocontractions in Banach Spaces
Cholamjiak Prasit,Suantai Suthep
Fixed Point Theory and Applications , 2010,
Abstract: We investigate the convergence of Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly convex Banach space with the Fréchet differentiable norm. Our results improve and extend the results obtained by Marino-Xu, Zhou, Osilike-Udomene, Zhang-Guo and the corresponding results. We also point out that the condition given by Chidume-Shahzad (2010) is not satisfied in a real Hilbert space. We show that their results still are true under a new condition.
Convergence Analysis for a System of Generalized Equilibrium Problems and a Countable Family of Strict Pseudocontractions
Cholamjiak Prasit,Suantai Suthep
Fixed Point Theory and Applications , 2011,
Abstract: We introduce a new iterative algorithm for a system of generalized equilibrium problems and a countable family of strict pseudocontractions in Hilbert spaces. We then prove that the sequence generated by the proposed algorithm converges strongly to a common element in the solutions set of a system of generalized equilibrium problems and the common fixed points set of an infinitely countable family of strict pseudocontractions.
Page 1 /56
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.