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Common fixed points of mappings satisfying implicit contractive conditions

Vasile Berinde* and Francesca Vetro

Author Affiliations

Department of Mathematics and Computer Science, Faculty of Sciences, North University of Baia Mare, 430122 Baia Mare, Romania

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Fixed Point Theory and Applications 2012, 2012:105 doi:10.1186/1687-1812-2012-105

Published: 24 June 2012

Abstract

In this article we obtain, in the setting of metric spaces or ordered metric spaces, coincidence point, and common fixed point theorems for self-mappings in a general class of contractions defined by an implicit relation. Our results unify, extend, generalize many related common fixed point theorems from the literature.

Mathematics Subject Classification (2000): 47H10, 54H25.

Keywords:
implicit relation; contraction; coincidence point; fixed point; common fixed point