Affiliation:
1. Department of Economics, Shiga University, Hikone, Shiga, Japan
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.
Publisher
National Library of Serbia
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