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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.

A general coincidence and common fixed point theorem for two hybrid pairs of mappings

Popa V.

Demonstratio Mathematica

2014

Vol. 47, nr 4

971--978

In this paper, a general coincidence and common fixed points theorem for two hybrid pairs of mappings satisfying property (E.A) is proved, generalizing the main results from [3] and [9].

Coincidence and common fixed point theorems via r-weak commutativity of type (AT)

Aliouche A., Popa V.

Fasciculi Mathematici

2009

Nr 41

5-16

We prove common fixed point theorems for two pairs of hybrid mappings satisfying implicit relations in complete metric spaces using the concept of R—weak commutativity of type At and we correct errors of [1], [3] and [8]. Our theorems generalize results of [1-3], [8], [12-16] and [21],