Approximation of common fixed points of a sequence of commuting generalized nonexpansive mappings

Abstract

It is the purpose of this paper to discuss the generalizations of nonexpansive mappings. We prove additional properties of these generalizations, particularly focusing on a sequence of commuting mappings satisfying condition B_γ,µ. We propose iterative algorithms to approximate a common fixed point of a sequence of commuting mappings satisfying condition B_γ,µ. With some mild assumptions on parameters, the convergence of these algorithms to a common fixed point of a sequence of commuting mappings satisfying condition B_γ,µ is also proved. Our results extend and improve many recent results in the literature.