DOI: 10.24193/fpt-ro.2021.1.25

Authors: M.O. Uba, E.E. Otubo and M.A. Onyido

Abstract: Let C be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space E with dual space E^*. A novel hybrid method for finding a solution of an equilibrium problem and a common element of fixed points for a family of a general class of nonlinear nonexpansive maps is constructed. The sequence of the method is proved to converge strongly to a common element of the family and a solution of the equilibrium problem. Finally, an application of our theorem complements, generalizes and extends some recent important results (Takahashi et al., Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 341 (2008), 276-286., Nakajo and Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semi-groups, J. Math. Anal. Appl. vol. 279 (2003), 372-379., Qin and Su, Strong convergence of monotone hybrid method for fixed point iteration process, J. Syst. Sci. and Complexity 21 (2008) 474-482., Klin-eam et al., Hybrid method for the equilibrium problem and a family of generalized nonexpansive mappings in Banach spaces, J. Nonlinear Sci. Appl. 9 (2016), 4963-4975 ).

Key Words and Phrases: Equilibrium problem, J_* fixed points, strong convergence.

2010 Mathematics Subject Classification: 47H09, 47H05, 47J25, 47J05, 47H10.

Published on-line: February 1st, 2021.

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