scholarly journals The Meir-Keeler Type for Solving Variational Inequalities and Fixed Points of Nonexpansive Semigroups in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Phayap Katchang ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Strong Convergence Theorem ◽  
Accretive Mapping ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Nonexpansive Semigroups ◽  
Strongly Accretive Mapping

The aim of this paper is to introduce a new iterative scheme for finding common solutions of the variational inequalities for an inverse strongly accretive mapping and the solutions of fixed point problems for nonexpansive semigroups by using the modified viscosity approximation method associate with Meir-Keeler type mappings and obtain some strong convergence theorem in a Banach spaces under some parameters controlling conditions. Our results extend and improve the recent results of Li and Gu (2010), Wangkeeree and Preechasilp (2012), Yao and Maruster (2011), and many others.

scholarly journals A New Composite General Iterative Scheme for Nonexpansive Semigroups in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Pongsakorn Sunthrayuth ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Duality Mapping ◽  
Strong Convergence Theorem ◽  
Iterative Approximation ◽  
Nonexpansive Semigroups ◽  
Weakly Continuous ◽  
Weakly Continuous Duality Mapping ◽  
Iterative Approximation Method

We introduce a new general composite iterative scheme for finding a common fixed point of nonexpansive semigroups in the framework of Banach spaces which admit a weakly continuous duality mapping. A strong convergence theorem of the purposed iterative approximation method is established under some certain control conditions. Our results improve and extend announced by many others.

scholarly journals On Common Solutions for Fixed-Point Problems of Two Infinite Families of Strictly Pseudocontractive Mappings and the System of Cocoercive Quasivariational Inclusions Problems in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-32
Author(s):  
Pattanapong Tianchai
Keyword(s):  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Pseudocontractive Mappings ◽  
Quasivariational Inclusions ◽  
Strictly Pseudocontractive Mappings

This paper is concerned with a common element of the set of common fixed points for two infinite families of strictly pseudocontractive mappings and the set of solutions of a system of cocoercive quasivariational inclusions problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a novel general iterative scheme based on the viscosity approximation method, and applicability of the results has shown difference with the results of many others existing in the current literature.

A halpern-type iteration for solving the split feasibility problem and the fixed point problem of Bregman relatively nonexpansive semigroup in Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3211-3227 ◽  
Author(s):  
Prasit Cholamjiak ◽  
Pongsakorn Sunthrayuth
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Nonexpansive Semigroup ◽  
Relatively Nonexpansive ◽  
The Split Feasibility Problem ◽  
Split Feasibility

We study the split feasibility problem (SFP) involving the fixed point problems (FPP) in the framework of p-uniformly convex and uniformly smooth Banach spaces. We propose a Halpern-type iterative scheme for solving the solution of SFP and FPP of Bregman relatively nonexpansive semigroup. Then we prove its strong convergence theorem of the sequences generated by our iterative scheme under implemented conditions. We finally provide some numerical examples and demonstrate the efficiency of the proposed algorithm. The obtained result of this paper complements many recent results in this direction.

scholarly journals A Viscosity Approximation Method with a Weakly Contractive Mapping of General Iterative Processes for Nonexpansive Semigroups in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Pongsakorn Sunthrayuth ◽  
Chanan Sudsukh ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Approximation Method ◽  
Contractive Mapping ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Iterative Processes ◽  
Weakly Contractive Mapping ◽  
Weakly Contractive

We introduce a new viscosity approximation method with a weakly contractive mapping of general iterative processes for finding common fixed point of nonexpansive semigroups {T(t):t∈ℝ+} in the framework of Banach spaces. We proved that under some mild conditions these iterative processes converge strongly to the common fixed point of {T(t):t∈ℝ+}, which is the unique solution of some variational inequality. The results obtained in this paper extend and improve on the recent results of Li et al. (2009), Chen and He (2007), and many others as special cases.

scholarly journals STRONG CONVERGENCE THEOREM FOR UNIFORMLY L-LIPSCHITZIAN MAPPING OF GREGUS TYPE IN BANACH SPACES

2021 ◽  
pp. 1259
Author(s):  
Olilima O. Joshua ◽  
Mogbademu A. Adesanmi ◽  
Adeniran T. Adefemi
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Real Banach Space ◽  
Iterative Scheme ◽  
Convergence Result ◽  
Strong Convergence Theorem ◽  
Lipschitzian Mapping ◽  
Mann Iterative Scheme

In this paper, we introduced a new mapping called Uniformly L-Lipschitzian mapping of Gregus type, and used the Mann iterative scheme to approximate the fixed point. A Strong convergence result for the sequence generated by the scheme is shown in real Banach space. Our result generalized and unifybmany recent results in this area  of research. In addition, using Java(jdk1.8.0_101), we give a numericalbexample to support our claim.

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