Open Access Research

Fixed point theorems for generalized contractions on GP-metric spaces

Nurcan Bilgili1, Erdal Karapınar2* and Peyman Salimi3

Author Affiliations

1 Department of Mathematics, Institute of Science and Technology, Gazi University, Ankara, 06500, Turkey

2 Department of Mathematics, Atilim University, İncek, Ankara, 06836, Turkey

3 Department of Mathematics, Sahand University of Technology, Tabriz, Iran

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Journal of Inequalities and Applications 2013, 2013:39 doi:10.1186/1029-242X-2013-39

Published: 6 February 2013

Abstract

In this paper, we present two fixed point theorems on mappings, defined on GP-complete GP-metric spaces, which satisfy a generalized contraction property determined by certain upper semi-continuous functions. Furthermore, we illustrate applications of our theorems with a number of examples. Inspired by the work of Jachymski, we also establish equivalences of certain auxiliary maps in the context of GP-complete GP-metric spaces.

MSC: 47H10, 54H25.

Keywords:
fixed point; partial metric space; GP-metric space