A modified Mann iterative scheme by generalized f-projection for a countable family of relatively quasi-nonexpansive mappings and a system of generalized mixed equilibrium problems
Siwaporn Saewan, Poom Kumam · Fixed Point Theory and Applications · 2011
Abstract The purpose of this paper is to introduce a new hybrid projection method based on modified Mann iterative scheme by the generalized f-projection operator for a countable family of relatively quasi-nonexpansive mappings and the solutions of the system of generalized mixed equilibrium problems. Furthermore, we prove the strong convergence theorem for a countable family of relatively quasi-nonexpansive mappings in a uniformly convex and uniform smooth Banach space. Finally, we also apply our results to the problem of finding zeros of B -monotone mappings and maximal monotone operators. The results presented in this paper generalize and improve some well-known results in the literature. 2000 Mathematics Subject Classification: 47H05; 47H09; 47H10.