From metric spaces to partial metric spaces

Bessem Samet,Calogero Vetro,Francesca Vetro

doi:10.1186/1687-1812-2013-5

Bessem Samet, Calogero Vetro + Show 1 more

Open Access

https://doi.org/10.1186/1687-1812-2013-5

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Abstract

Motivated by experience from computer science, Matthews (1994) introduced a nonzero self-distance called a partial metric. He also extended the Banach contraction principle to the setting of partial metric spaces. In this paper, we show that fixed point theorems on partial metric spaces (including the Matthews fixed point theorem) can be deduced from fixed point theorems on metric spaces. New fixed point theorems on metric spaces are established and analogous results on partial metric spaces are deduced. MSC:47H10, 54H25.

Highlights

Introduction and preliminariesOver the last decades, fixed point theory has been revealed as a very powerful tool in the study of nonlinear phenomena
In, Matthews [ ] introduced the notion of partial metric space as a part of the study of denotational semantics of dataflow networks and showed that the Banach contraction principle can be generalized to the partial metric context for applications in program verification
In this paper, motivated and inspired by Rus [ ], we present new fixed point theorems on complete metric spaces

Summary

Introduction

Introduction and preliminariesOver the last decades, fixed point theory has been revealed as a very powerful tool in the study of nonlinear phenomena. Many researchers studied fixed point theorems in partial metric spaces. (see [ ]) Let (X, p) be a partial metric space and {xn} be a sequence in X. (see [ ]) Let (X, p) be a partial metric space.

Results

Conclusion