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

F.A. Khan, K.R. Kazmi, F.M. Alharbi, M. Dilshad

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.


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How to Cite this Article:

F.A. Khan, K.R. Kazmi, F.M. Alharbi, M. Dilshad, Convergence and stability analysis of iterative algorithm for a generalized set-valued mixed equilibrium problem, Journal of Mathematical and Computational Science, Vol 8, No 2 (2018), 241-252

Copyright © 2018 F.A. Khan, K.R. Kazmi, F.M. Alharbi, M. Dilshad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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