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  • Author: Kristaq Kikina x
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Abstract

In this paper, we obtain some new fixed point theorems in generalized metric spaces for maps satisfying an implicit relation. The obtained results unify, generalize, enrich, complement and extend a multitude of related fixed point theorems from metric spaces to generalized metric spaces.

Abstract

A fixed point theorem for three mappings on a metric space into itself is proved. This result extends the results obtained in [] from two mappings to three mappings, and after that, a generalization for an arbitrary number of mappings is obtained. As corollaries of these results we obtain the extending of Theorems of Nešić, Rhoades, Chatterjea, Rus and Kannan for an arbitrary number of mappings.

Abstract

A generalized metric space has been defined by Branciari as a metric space in which the triangle inequality is replaced by a more general inequality. Subsequently, some classical metric fixed point theorems have been transferred to such a space. In this paper, we continue in this direction and prove a version of Fisher’s fixed point theorem in generalized metric spaces.