Compatible mappings of type (C) and common fixed point theorems of Gregus type

A collection of fixed point theorems is generalized by replacing hypothesized commutativity or weak commutativity of functions involved by compatibility.

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Some fixed point theorems for compatible maps

The authors prove common flxed point theorems in metric spaces for four mappings satisfying an implicit relation, without decreasing assumption, using the concept of weak compatibility. These generalize two theorems of V. Popa, a theorem of M. Imdad, S. Kumar and M. S. Khan, a theorem of H. Bouhadjera and a theorem of A. Djoudi and A. Aliouche, respectively.

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Common fixed point theorems for mappings satisfying an implicit relation without decreasing assumption

/pdf/on-some-discontinuous-fixed-point-mappings-in-convex-metric-1fjlwjq82d.pdf

On some discontinuous fixed point mappings in convex metric spaces

This paper presents a survey that aims to provide a brief historical account of the development through the definitions and comparison of weaker forms of commuting mappings set brought together from some applications oriented point of view.

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A comparison of various noncommuting conditions in metric fixed point theory and their applications

In this note, we present a common fixed point theorem of type for two pairs of compatible mappings by using a single hypothesis on the existence of 'non-Archimedian trisection-points'. In the sequel, our result improve the results of Davies and Sessa, Davies, Jungck and many others.

H.K. Pathak

Papers

A Common Fixed Point Theorem of $Gregu{\check{s}}$ Type for Two Pairs of Compatible Mappings