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Journal of Function Spaces
Volume 2014, Article ID 416187, 8 pages
http://dx.doi.org/10.1155/2014/416187
Research Article

Fixed Point Theorems for Contractions of Rational Type with PPF Dependence in Banach Spaces

1Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain
2Department of Mathematics, Rzeszów University of Technology, Aleja Powstanców Warszawy 8, 35-959 Rzeszów, Poland

Received 10 April 2014; Accepted 24 May 2014; Published 9 June 2014

Academic Editor: Józef Banaś

Copyright © 2014 J. Rocha 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 prove the existence of the PPF dependent fixed point in the Razumikhin class for contractions of rational type in Banach spaces, by using a general class of pairs of functions. Our result has as particular cases a great number of interesting consequences which extend and generalize some results appearing in the literature.