A generalization of the common fixed point theorem for normally 2-generalized hybrid mappings in Hilbert spaces

Abstract

In this paper, we prove a common fixed point theorem for commutative nonlinear mappings that jointly satisfy a certain condition. A required condition is given as a convex combination of those of a well-known class of nonlinear mappings. From the main theorem of this paper, the common fixed point theorem for nonexpansive mappings, generalized hybrid mappings, and normally 2-generalized hybrid mappings are uniformly derived as corollaries. Our approach expands the applicable range of mappings for existing fixed point theorems to be effective. Using specific mappings, we illustrate the effectiveness.