Common fixed points of monotone ρ-nonexpansive semigroup in modular spaces

Abstract

Abstract In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in uniformly convex modular spaces and modular spaces. Then we introduce an iteration algorithm to approximate a common fixed point for the same class of semigroups.

Keywords

• Fixed point
• Modular space
• Uniform asymptotic regular
• Monotone ρ-nonexpansive semigroups
• Uniformly convex
• Uniformly convex in every direction