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Fixed point theorems on generalized metric spaces for mappings in a class of almost φ-contractions

Kikina L., Kikina K.

Demonstratio Mathematica

2015

Vol. 48, nr 3

440--451

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.

A fixed point theorem in generalized metric spaces

Kikina L., Kikina K.

Demonstratio Mathematica

2013

Vol. 46, nr 1

181--190

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.

Fixed points for k mappings on a complete metric spaces

Kikina L., Kikina K.

Demonstratio Mathematica

2011

Vol. 44, nr 2

349--357

A fixed point theorem for three mappings on a metric space into itself is proved. This result extends the results obtained in [1] from two mappings to three map pings, 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 Nesic, Rhoades, Chatterjea, Rus and Kannan for an arbitrary number of mappings.