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Mathematics > Optimization and Control

arXiv:1805.02499 (math)
[Submitted on 4 May 2018]

Title:Weak convergence theorems for a symmetric generalized hybrid mapping and an equilibrium problem

Authors:Bui Van Dinh, Nguyen Ngoc Hai, Do Sang Kim
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Abstract: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.
Comments: arXiv admin note: text overlap with arXiv:1508.03907
Subjects: Optimization and Control (math.OC)
MSC classes: $47$H$06$, $47$H$09$, $47$H$10$, $47$J$05$, $47$J$25$
Cite as: arXiv:1805.02499 [math.OC]
  (or arXiv:1805.02499v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1805.02499

Submission history

From: Dinh Bui Van [view email]
[v1] Fri, 4 May 2018 08:05:58 UTC (21 KB)
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