Nonlinear Contractions in 0‐Complete Partial Metric Spaces

Abd Ghafur Bin Ahmad,Stojan Radenović,Zaid Mohammed Fadail,Vesna Ćojbašić Rajić

doi:10.1155/2012/451239

Abd Ghafur Bin Ahmad, Stojan Radenović + Show 2 more

Open Access

https://doi.org/10.1155/2012/451239

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Abstract

Using the setting of 0‐complete partial metric spaces, some common fixed point results of maps that satisfy the nonlinear contractive conditions are obtained. These results generalize and improve the existing fixed point results in the literature in the sense that weaker conditions are used. An example shows how our result can be used when the corresponding result in standard metric cannot.

Highlights

Introduction and PreliminariesMatthews 1 generalized the concept of a metric space by introducing partial metric spaces
We obtain some common fixed point results defined on 0-complete partial metric spaces
From Corollary 2.8 follows the theorem proved by Jungck 31, where we consider a 0-complete partial metric space instead of a complete metric space, under the assumption that T and f are commuting mappings

Summary

Introduction

Introduction and PreliminariesMatthews 1 generalized the concept of a metric space by introducing partial metric spaces. We obtain some common fixed point results defined on 0-complete partial metric spaces. From Lemma 1.6 follows that this is a unique common fixed point of T and f.

Objectives

Results

Conclusion