Inertial-Viscosity-Type Algorithms for Solving Generalized Equilibrium and Fixed Point Problems in Hilbert Spaces

被引:7
作者
Taiwo, Adeolu [1 ]
Mewomo, Oluwatosin Temitope [1 ]
机构
[1] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, Durban, South Africa
基金
新加坡国家研究基金会;
关键词
Fixed point problem; Generalized equilibrium problem; Multivalued non-expansive mapping; Hilbert spaces; STRONG-CONVERGENCE THEOREMS; VARIATIONAL INEQUALITY; NONEXPANSIVE-MAPPINGS; COMMON SOLUTION; APPROXIMATION;
D O I
10.1007/s10013-021-00485-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we introduce a new algorithm of inertial form for solving Split Generalized Equilibrium Problem (SGEP) and Fixed Point Problem (FPP) of multivalued nonexpansive mappings in real Hilbert spaces. Motivated by the viscosity-type method, we incorporate the inertial technique to accelerate the convergence of the proposed method. Here, the viscosity term is a function of the inertial extrapolation sequence and some assumptions on the bifunctions are dispensed with. Under standard and mild assumption of monotonicity and upper hemicontinuity of the SGEP associated mappings, we establish the strong convergence of the scheme which also solves a Variational Inequality Problem (VIP). A numerical example is presented to illustrate the effectiveness and performance of our method as well as comparing it with a related method and conventional inertial-viscosity-type algorithm in the literature.
引用
收藏
页码:125 / 149
页数:25
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