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2013•Fixed Point Theory and ApplicationsOpen access

Faintly compatible mappings and common fixed points

Ravindra Kishor Bisht, Naseer Shahzad

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Abstract

In this paper we introduce a generalization of the concept of compatible mappings, and using that condition, we obtain some new fixed point theorems under both contractive and noncontractive conditions, which may allow the existence of a common fixed point or the existence of multiple fixed or coincidence points. We also manifest that the new concept is a necessary condition for the existence of a common fixed point. MSC: 47H10, 54H25.

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What this paper is about

In this paper we introduce a generalization of the concept of compatible mappings, and using that condition, we obtain some new fixed point theorems under both contractive and noncontractive conditions, which may allow the existence of a common fixed point or the existence of multiple fixed or coincidence points. We also manifest that the new concept is a necessary condition for the existence of a common fixed point. MSC: 47H10, 54H25.

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Available abstract

In this paper we introduce a generalization of the concept of compatible mappings, and using that condition, we obtain some new fixed point theorems under both contractive and noncontractive conditions, which may allow the existence of a common fixed point or the existence of multiple fixed or coincidence points. We also manifest that the new concept is a necessary condition for the existence of a common fixed point. MSC: 47H10, 54H25.

Key concepts: Coincidence point, Fixed point, Coincidence, Mathematics, Differential geometry, Generalization, Fixed-point theorem, Discrete mathematics

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