APPROXIMATING COMMON SOLUTION OF A SYSTEM OF EQUILIBRIUM PROBLEMS IN BANACH SPACES

作者：Naraghirad Eskandar^*; Takahashi Wataru

来源：Journal of Nonlinear and Convex Analysis, 2015, 16(5): 943-964.

• Equilibrium problem
• fixed point
• strong convergence
• quasi-phi-nonexpansive mapping
• Halpern-type iterative scheme

In this paper we introduce new Halpern-type iterative algorithms for finding a common solution of a system of equilibrium problems in Banach spaces. We prove strong convergence of a modified Halpern-type scheme to an element of the set of common solution of a system of equilibrium problems in a reflexive Banach space and provide an affirmative answer to an open question raised by Zegeye and Shahzad in their final remark of [Zegeye and Shahzad, Approximating common solution of variational inequality problems for two monotone mappings in Banach spaces, Optimization Letters, 5 (2011) 691-704]. This scheme has an advantage that we do not use any generalized projection of a point on the intersection of closed and convex sets which creates some difficulties in a practical calculation of the iterative sequence. Some application of our results to the problem of finding a minimizer of a continuously Frechet differentiable and convex function in a Banach space is presented. Our results improve and generalize many known results in the current literature.

• 出版日期2015