Generalized common fixed point theorem for generalized hybrid mappings in Hilbert spaces

Abstract

In this article, we prove a common fixed point theorem for commutative nonlinear mappings that jointly satisfy a certain condition. From the main theorem, a common fixed point theorem for commutative generalized hybrid mappings is derived as a special case. Our novel approach significantly expands the applicable range of mappings for well-known fixed point theorems to be effective. Examples are presented to explicitly illustrate this contribution.

Keywords

• common fixed point theorem
• generalized hybrid mappings
• nonexpansive mappings
• nonspreading mappings
• hilbert space
• 47h10