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

Kondo Atsumasa

Demonstratio Mathematica

2022

Vol. 55, nr 1

752--759

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.