A novel hybrid method for equilibrium problem and a countable family of generalized nonexpansive-type maps with applications
Markjoe O. Uba, Emmanuel Ezzaka Otubo, Maria A. Onyido · Fixed Point Theory · 2021
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,