On split generalised mixed equilibrium problems and fixed-point problems with no prior knowledge of operator norm

被引：28

作者：

Ogbuisi, F. U. ^{[1
,2
]}

Mewomo, O. T. ^{[1
]}

机构：

[1] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, Durban, South Africa

[2] DST NRF Ctr Excellence Math & Stat Sci CoE MaSS, Johannesburg, South Africa

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2017年 / 19卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

kappa-Pseudocontraction; Hilbert space; split generalised mixed equilibrium problem; fixed point; bounded linear operator; strong convergence; STRONG-CONVERGENCE THEOREMS; STRICT PSEUDO-CONTRACTIONS; HYBRID ITERATIVE METHOD; VARIATIONAL-INEQUALITIES; APPROXIMATION METHOD; EXTRAGRADIENT METHOD; MAPPINGS;

D O I：

10.1007/s11784-016-0397-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to introduce an iterative algorithm that does not require any knowledge of the operator norm for approximating a solution of a split generalised mixed equilibrium problem which is also a fixed point of a -strictly pseudocontractive mapping. Furthermore, a strong convergence theorem for approximating a common solution of a split generalised mixed equilibrium problem and a fixed-point problem for -strictly pseudocontractive mapping was stated and proved in the frame work of Hilbert spaces.

引用

页码：2109 / 2128

页数：20

共 32 条

[1] Blum E., 1994, Math. student, V63, P123
[2] Strong Convergence Algorithm for Split Equilibrium Problems and Hierarchical Fixed Point Problems
Bnouhachem, Abdellah
[J]. SCIENTIFIC WORLD JOURNAL, 2014,
[3] CONSTRUCTION OF FIXED POINTS OF NONLINEAR MAPPINGS IN HILBERT SPACE
BROWDER, FE
PETRYSHY.WV
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1967, 20 (02) : 197 - &
[4] Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces
Cholamjiak, Prasit
Suantai, Suthep
[J]. ABSTRACT AND APPLIED ANALYSIS, 2010,
[5] Combettes PL, 2005, J NONLINEAR CONVEX A, V6, P117
[6] A hierarchical presentation of operators with fixed points on Hilbert spaces
Crombez, G.
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2006, 27 (3-4) : 259 - 277
[7] A geometrical look at iterative methods for operators with fixed points
Crombez, G
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2005, 26 (02) : 157 - 175
[8] Ferreira P. J. S. G., REV DETUA, V1
[9] The split equilibrium problem and its convergence algorithms
He, Zhenhua
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012,
[10] Hendrickx J. M., 2010, ARXIV09081397V3CSCC

← 1 2 3 4 →