Open AccessWeak convergence theorems for symmetric generalized hybrid mappings and equilibrium problems
Author(s) -
Do Sang Kim,
Nguyễn Ngọc Hải,
Bui Van Dinh
Publication year - 2022
Publication title -
numerical algebra, control and optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.303
H-Index - 20
eISSN - 2155-3289
pISSN - 2155-3297
DOI - 10.3934/naco.2021051
Subject(s) - hilbert space , mathematics , convergence (economics) , fixed point , set (abstract data type) , algorithm , iterative method , point (geometry) , mathematical optimization , pure mathematics , computer science , mathematical analysis , economics , programming language , geometry , economic growth
In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method can be considered as an combination of Ishikawa's process with the proximal point algorithm, the extragradient algorithm with or without linesearch. Under certain conditions on parameters, the iteration sequences generated by the proposed methods are proved to be weakly convergent to a solution of the problem. These results extend the previous results given in the literature. A numerical example is also provided to illustrate the proposed algorithms.