On Weakly (C, ψ, ϕ)‐Contractive Mappings in Ordered Partial Metric Spaces

Erdal Karapınar,Wasfi Shatanawi

doi:10.1155/2012/495892

Erdal Karapınar, Wasfi Shatanawi

Open Access

https://doi.org/10.1155/2012/495892

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Abstract

We introduce the notion of weakly (C, ψ, ϕ)‐contractive mappings in ordered partial metric spaces and prove some common fixed point theorems for such contractive mappings in the context of partially ordered partial metric spaces under certain conditions. We give some common fixed point results of integral type as an application of our main theorem. Also, we give an example and an application of integral equation to support the useability of our results.

Highlights

Introduction and PreliminariesIn 1994, Matthews 1 introduced the notion of a partial metric space as a generalization of the usual metric space
Choudhury 34 introduced the concept of weakly C-contractive mapping as a generalization of C-contractive mapping and prove that every weakly C-contractive mapping in a complete metric space has a unique fixed point
Harjani et al 35 announced some fixed point results for weakly C-contractive mappings in a complete metric space endowed with a partial order

Summary

Introduction and Preliminaries

In 1994, Matthews 1 introduced the notion of a partial metric space as a generalization of the usual metric space. D x, x is not necessarily equal a zero In this interesting paper, Matthews 1 prove the Banach contraction mapping principle in the frame of partial metric spaces. Choudhury 34 introduced the concept of weakly C-contractive mapping as a generalization of C-contractive mapping and prove that every weakly C-contractive mapping in a complete metric space has a unique fixed point. Harjani et al 35 announced some fixed point results for weakly C-contractive mappings in a complete metric space endowed with a partial order. We introduce the concept of weakly C, ψ, φ -contractive mappings in ordered partial metric spaces, and we prove some existence theorems of common fixed point for such mapping in the context of complete partial metric spaces under certain conditions

The Main Result

Application