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

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  • Deepak Singh
  • Varsha Chauhan
  • R. Wangkeeree

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.

Suggested Citation

  • Deepak Singh & Varsha Chauhan & R. Wangkeeree, 2017. "Geraghty Type Generalized -Contractions and Related Applications in Partial -Metric Spaces," International Journal of Analysis, Hindawi, vol. 2017, pages 1-14, March.
    • Handle: RePEc:hin:ijanal:8247925
    DOI: 10.1155/2017/8247925
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