Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 458086, 16 pages
doi:10.1155/2010/458086
Research Article

On Mappings with Contractive Iterate at a Point in Generalized Metric Spaces

Ljiljana Gajić and Zagorka Lozanov-Crvenković

Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovća 4, 21000 Novi Sad, Serbia

Received 7 September 2010; Revised 1 December 2010; Accepted 29 December 2010

Academic Editor: B. Rhoades

Copyright © 2010 Ljiljana Gajić and Zagorka Lozanov-Crvenković. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using the setting of generalized metric space, the so-called G-metric space, fixed point theorems for mappings with a contractive and a generalized contractive iterate at a point are proved. These results generalize some comparable results in the literature. A common fixed point result is also proved.