On weak and strong convergence results for generalized equilibrium variational inclusion problems in Hilbert spaces

Advances in Difference Equations

article

Rezapour, Shahram¹  Zakeri, Seyyed Hasan⁴ 

[1] Institute of Research and Development, Duy Tan University;Faculty of Natural Sciences, Duy Tan University;Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics, Azarbaijan Shahid Madani University

关键词: Generalized equilibrium problems;    Hilbert spaces;    Inverse strongly monotone map;    Maximal monotone operator;    Nonexpansive mappings;    Variational inclusion;   

DOI  :  10.1186/s13662-020-02927-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We introduce a new iterative method for finding a common element of the set of fixed points of pseudo-contractive mapping, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. We provide some results about strongly and weakly convergent of the iterative scheme sequence to a point$p\in \varOmega $ which is the unique solution of a variational inequality, where Ω is an intersection of set as given by${\varOmega }=F(S)\cap (A+B)^{-1}(0) \cap N^{-1}(0)\cap \operatorname{GEP}(F,M)\neq \emptyset $ . This gives us a common solution. Also, We show that our results extend some published recent results in this field. Finally, we provide an example to illustrate our main result.

【 授权许可】

CC BY