Strong convergence theorems for equilibrium problems involving Bregman functions in Banach spaces

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Published: Jun 30, 2017
DOI: https://doi.org/10.5556/j.tkjm.48.2017.2299
Keywords:
Bregman function fixed point strong convergence equilibrium problem Halpern-type iterative scheme

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Eskandar Naraghirad
Sara Timnak

Abstract

In this paper, using Bregman functions, we introduce new Halpern-type iterative algorithms for finding a solution of an equilibrium problem in Banach spaces. We prove the strong convergence of a modified Halpern-type scheme to an element of the set of solution of an equilibrium problem in a reflexive Banach space. This scheme has an advantage that we do not use any Bregman projection of a point on the intersection of closed and convex sets in a practical calculation of the iterative sequence. Finally, some application of our results to the problem of finding a minimizer of a continuously Fr\'{e}chet differentiable and convex function in a Banach space is presented. Our results improve and generalize many known results in the current literature.

Article Details

How to Cite
Naraghirad, E., & Timnak, S. (2017). Strong convergence theorems for equilibrium problems involving Bregman functions in Banach spaces. Tamkang Journal of Mathematics, 48(2), 159–184. https://doi.org/10.5556/j.tkjm.48.2017.2299
Issue
Vol. 48 No. 2 (2017)
Section
Papers
Author Biographies

Eskandar Naraghirad

Department of Mathematics, Yasouj University, Yasouj 75918, Iran and Department of AppliedMathematics, National Sun Yat-sen University, Kaohsiung, 804, Taiwan.

Sara Timnak

Department of Mathematics, Yasouj University, Yasouj 75918, Iran.

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