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This paper is concerned with a common element of the set of common fixed point for a discrete asymptotically strictly pseudocontractive semigroup and the set of solutions of the mixed equilibrium problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a general iterative scheme based on the shrinking projection method which extends and improves the corresponding ones due to Kim [Proceedings of the Asian Conference on Nonlinear Analysis and Optimization (Matsue, Japan, 2008), 139–162].

isrn mathematical physics/isrn mathematical analysis

Shrinking Projection Method of Common Fixed Point Problems for Discrete Asymptotically Strictly Pseudocontractive Semigroups and Mixed Equilibrium Problems in Hilbert Spaces