ON SPLIT EQUALITY GENERALIZED EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF BREGMAN RELATIVELY NONEXPANSIVE SEMIGROUPS

被引：0

作者：

Abass H.A. ^{[1
]}

Izuchukwu C. ^{[1
]}

Mewomo O.T. ^{[1
]}

机构：

[1] School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban

来源：

Journal of Applied and Numerical Optimization | 2022年 / 4卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

Bregman relatively nonexpansive semigroup; Generalized equilibrium problem; p-uniformly convex and uniformly smooth Banach spaces; Split feasibility problem;

D O I：

10.23952/jano.4.2022.3.04

中图分类号：

学科分类号：

摘要：

In this paper, we introduce a new split inverse problem called the split equality generalized equilibrium problem which is more general than the split feasibility problem, the split equilibrium problem, and the split equality equilibrium problem. We develop an iterative algorithm for approximating a common solution of this problem and the split equality fixed point problem for Bregman relatively nonexpansive semigroups in p-uniformly convex and uniformly smooth Banach spaces. Using our iterative algorithm, we prove a strong convergence theorem and investigate a split equality convex optimization problem as an application. Finally, we present some numerical experiments to demonstrate the applicability of our proposed method. © 2022 Journal of Applied and Numerical Optimization.

引用

页码：357 / 380

页数：23

共 34 条

[1] Godwin E.C., Alakoya T.O., Mewomo O.T., Yao J.-C., Relaxed inertial Tseng extragradient method for variational inequality and fixed point problems, Appl. Anal, (2022)
[2] Shimizu K., Hishinuma K., Iiduka H., Parallel computing proximal method for nonsmooth convex optimization with fixed point constraints of quasi-nonexpansive mappings, Appl. Set-Valued Anal. Optim, 2, pp. 1-17, (2020)
[3] Luo C., Ji H., Li Y., Utility-based multi-service bandwidth allocation in the 4G heterogeneous wireless networks, IEEE Wireless Communication and Networking Conference, (2009)
[4] Blum E., Oettli W., From Optimization and variational inequalities to equilibrium problems, Math. Stud, 63, pp. 123-145, (1994)
[5] Ceng L.C., A subgradient-extragradient method for bilevel equilibrium problems with the constraints of variational inclusion systems and fixed point problems, Commun. Optim. Theory, 2021, (2021)
[6] Olona M.A., Alakoya T.O., Owolabi A.O.-E., Mewomo O.T., Inertial algorithm for solving equilibrium, variational inclusion and fixed point problems for an infinite family of strict pseudocontractive mappings, J. Nonlinear Funct. Anal, 2021, 2021
[7] Alakoya T.O., Mewomo O.T., Shehu Y., Strong convergence results for quasimonotone variational inequalities, Math. Methods Oper. Res, 95, pp. 249-279, (2022)
[8] Alakoya T.O., Taiwo A., Mewomo O.T., On system of split generalised mixed equilibrium and fixed point problems for multivalued mappings with no prior knowledge of operator norm, Fixed Point Theory, 23, pp. 45-74, (2022)
[9] Godwin E.C., Mewomo O.T., Araka N.A., Okeke G.A., Ezeamara G.C., Inertial scheme for solving two level variational inequality and fixed point problem involving pseudomonotone and ρ-demimetric mappings, Appl. Set-Valued Anal. Optim, 4, pp. 251-267, (2022)
[10] Ogwo G.N., Alakoya T.O., Mewomo O.T., Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems, Optimization, (2021)

← 1 2 3 4 →