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Journal of Function Spaces
Volume 2015, Article ID 136306, 13 pages
http://dx.doi.org/10.1155/2015/136306
Research Article

New Dependent Fixed Point Theorems for Suzuki Type -Contractions

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Received 30 December 2014; Revised 6 March 2015; Accepted 9 March 2015

Academic Editor: Calogero Vetro

Copyright © 2015 M. A. Kutbi et al. 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

We introduce new concepts of an -GF-contractive nonself-mapping, a weak -GF-contractive nonself-mapping, a generalized -GF-contractive nonself-mapping, and Suzuki type GF-contractions and establish the existence of PPF dependent fixed point theorems for such kind of contractive nonself-mappings in the Razumikhin class. As applications of our results, we derive some PPF dependent fixed point theorems for GF-contractive nonself-mappings whenever the range space is endowed with a graph or a partial order. The obtained results generalize, extend, and modify some PPF dependent fixed point results in the literature.