A NEW HYBRID METHOD FOR SOLVING GENERALIZED EQUILIBRIUM PROBLEM AND COMMON FIXED POINTS OF ASYMPTOTICALLY QUASI NONEXPANSIVE MAPPINGS IN BANACH SPACEScally quasi nonexpansive mappings in Banach spaces

Abstract

In this paper, we introduce a new hybrid projection iterative scheme based on the shrinking projection method for two asymptotically quasi-f-nonexpansive mappings, for finding a common element of the set of solutions of the generalized mixed equilibrium problems and the set of common fixed points of two asymptotically quasi-f-nonexpansive mappings in Banach spaces. The results obtained in this paper improve and extend the recent ones announced by Matsushita and Takahashi [ S. Matsushita, W. Takahashi, Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces, Fixed point theory Appl. (2004), 2004, 37-47], Qin et al. [X. Qin, S.Y. Cho, S.M Kang, On hybrid projection methods for asymptotically quasi-f-nonexpansive mappings, Applied Mathematics and Computation215 (2010) 38743883], and Chang, Lee and Chan [S.-s. Chang, H.W. Joseph Lee, C.K.Chan, A new hybrid method for solving generalized equilibrium problem variational inequality and common fixed point in Banach spaces with applications, Nonlinear Analysis (2010), doi:10.1016/j.na.2010.06.006] and many others.