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

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.

Keywords


Bregman function; fixed point; strong convergence; equilibrium problem; Halpern-type iterative scheme

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References


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DOI: http://dx.doi.org/10.5556/j.tkjm.48.2017.2299

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