Convergence and stability analysis of iterative algorithm for a generalized set-valued mixed equilibrium problem

Abstract

In this paper, we consider a generalized set-valued mixed equilibrium problem (in short, GSMEP) in real Hilbert space. Related to GSMEP, we consider a generalized Wiener-Hopf equation problem (in short, GWHEP) and show an equivalence relation between them. Further, we give a fixed-point formulation of GWHEP and construct an iterative algorithm for GWHEP. Furthermore, we extend the notion of stability given by Harder and Hick [3] and prove the existence of a solution of GWHEP and discuss the convergence and stability analysis of the iterative algorithm. Our results can be viewed as a refinement and improvement of some known results in the literature.