Solution Of A Class Of Equilibrium Problems And Variational Inequalities In Fc Spaces

Keywords

Auxiliary principle technique; FC space; Generalized weakly relaxed η- α monotonicity; Mixed variational-like inequality; Proximal iterative scheme

Abstract

In this paper, we study a class of mixed variational-like inequalities with respect to generalized weakly relaxed η- α monotone mappings, involving nonlinear bifunctions, in finitely continuous topological space, in short FC space. Existence of the solution to the problem is established relaxing convexity and linearity condition by using generalized RKKM theorem. We have proposed a proximal iterative scheme using auxiliary principle technique. Solvability of the auxiliary variational inequality problem is established. Finally convergence of the iterates to the exact solution is proved. Some results with application to equilibrium problem are also discussed.

Publication Date

10-1-2018

Publication Title

Annals of Operations Research

Volume

269

Issue

1-2

Number of Pages

565-582

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10479-017-2506-3

Socpus ID

85018739864 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85018739864

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