A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi‐Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems
Siwaporn Saewan, Poom Kumam · Abstract and Applied Analysis · 2010
We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi‐nonexpansive mappings, the set of the variational inequality for an α ‐inverse‐strongly monotone operator, the set of solutions of the generalized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2 uniformly convex and uniformly smooth Banach space. The results presented in this paper improve and extend some recent results.