Table of Contents
International Journal of Analysis
Volume 2017, Article ID 8247925, 14 pages
https://doi.org/10.1155/2017/8247925
Research Article

Geraghty Type Generalized -Contractions and Related Applications in Partial -Metric Spaces

1Department of Applied Sciences, NITTTR, Ministry of HRD, Government of India, Bhopal 462002, India
2Department of Mathematics, NRI Institute of Research & Technology, Bhopal, India
3Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Correspondence should be addressed to R. Wangkeeree; ht.ca.un@wnaibar

Received 31 October 2016; Accepted 6 December 2016; Published 15 March 2017

Academic Editor: Ying Hu

Copyright © 2017 Deepak Singh 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

The purpose of this paper is to introduce new concepts of -admissible Geraghty type generalized -contraction and to prove that some fixed point results for such mappings are in the perspective of partial -metric space. As an application, we inaugurate new fixed point results for Geraghty type generalized graphic -contraction defined on partial metric space endowed with a directed graph. On the other hand, one more application to the existence and uniqueness of a solution for the first-order periodic boundary value problem is also provided. Our findings encompass various generalizations of the Banach contraction principle on metric space, partial metric space, and partial -metric space. Moreover, some examples are presented to illustrate the usability of the new theory.