A MODIFIED MANN ITERATIVE SCHEME FOR A SEQUENCE OF NONEXPANSIVE MAPPINGS AND A MONOTONE MAPPING WITH APPLICATIONS

被引：0

作者：

Bagherboum, M. ^{[1
]}

Razani, A. ^{[1
]}

机构：

[1] Islamic Azad Univ, Coll Basic Sci, Dept Math, Karaj Branch, Alborz, Iran

来源：

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2014年 / 40卷 / 04期

关键词：

Equilibrium problem; maximal monotone operator; strictly pseudocontractive mapping; W-mapping; VISCOSITY APPROXIMATION METHODS; FINDING COMMON SOLUTIONS; FIXED-POINTS; CONVERGENCE THEOREMS; WEAK-CONVERGENCE; COUNTABLE FAMILY; EQUILIBRIUM; OPERATORS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a real Hilbert space, an iterative scheme is considered to obtain strong convergence which is an essential tool to find a common fixed point for a countable family of nonexpansive mappings and the solution of a variational inequality problem governed by a monotone mapping. In this paper, we give a procedure which results in developing Shehu's result to solve equilibrium problem. Then, we state more applications of this procedure. Finally, we investigate some numerical examples which hold in our main results.

引用

页码：823 / 849

页数：27

共 30 条

[1] [Anonymous], 1997, ANN U MARIAC CURIE S
[2] Weak convergence of an iterative sequence for accretive operators in Banach spaces
Aoyama, Koji
Iiduka, Hideaki
Takahashi, Wataru
[J]. FIXED POINT THEORY AND APPLICATIONS, 2006, 2006 (1)
[3] Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
Aoyama, Koji
Kimura, Yasunori
Takahashi, Wataru
Toyoda, Masashi
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (08) : 2350 - 2360
[4] An iterative method for finding common solutions of equilibrium and fixed point problems
Colao, Vittorio
Marino, Giuseppe
Xu, Hong-Kun
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 344 (01) : 340 - 352
[5] An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings
Colao, Vittorio
Lopez-Acedo, Genaro
Marino, Giuseppe
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (7-8) : 2708 - 2715
[6] Viscosity approximation methods for monotone mappings and a countable family of nonexpansive mappings
Kumam, Poom
Plubtieng, Somyot
[J]. MATHEMATICA SLOVACA, 2011, 61 (02) : 257 - 274
[7] On a Hybrid Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem of a Family of Quasi-φ-Asymptotically Nonexpansive Mappings in Banach Spaces
Liu, Min
Chang, Shih-sen
Zuo, Ping
[J]. FIXED POINT THEORY AND APPLICATIONS, 2010,
[8] MEAN VALUE METHODS IN ITERATION
MANN, WR
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 4 (03) : 506 - 510
[9] A strong convergence theorem for relatively nonexpansive mappings in a Banach space
Matsushita, SY
Takahashi, W
[J]. JOURNAL OF APPROXIMATION THEORY, 2005, 134 (02) : 257 - 266
[10] Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings
Nakprasit, Kittikorn
Nilsrakoo, Weerayuth
Saejung, Satit
[J]. FIXED POINT THEORY AND APPLICATIONS, 2008, 2008 (1)

← 1 2 3 →