Some fixed point results via R-functions

Antonella Nastasi,Stojan Radenović,Pasquale Vetro

doi:10.1186/s13663-016-0572-x

Antonella Nastasi, Stojan Radenović + Show 1 more

Open Access

https://doi.org/10.1186/s13663-016-0572-x

Copy DOI

Abstract

AbstractWe establish existence and uniqueness of fixed points for a new class of mappings, by using R-functions and lower semi-continuous functions in the setting of metric spaces. As consequences of this results, we obtain several known fixed point results, in metric and partial metric spaces. An example is given to support the new theory. A homotopy result for operators on a set endowed with a metric is given as application.

Highlights

Metric fixed point theory is a fundamental topic, which gives basic methods and notions for establish practical problems in mathematics and the other sciences
We consider the existence of solutions of mathematical problems reducible to equivalent fixed point problems
The notion of partial metric space was introduced in by Matthews [ ] as a part of the study of denotational semantics of data for networks. This setting is a generalization of the classical concept of metric space

Summary

Introduction

Metric fixed point theory is a fundamental topic, which gives basic methods and notions for establish practical problems in mathematics and the other sciences. This concept is a new type of nonlinear contraction defined by using a specific function, called simulation function They proved the existence and uniqueness of fixed points for Z-contraction mappings This notion is a new type of nonlinear contraction defined by using a specific function called R-function They proved the existence and uniqueness of fixed points for R-contraction mappings (see [ ], Theorem ). We establish a result of existence and uniqueness of a fixed point for R-λ-contractions that belong to {x ∈ Z : λ(x) = }. We present some particular results of fixed point in metric spaces, by choosing an appropriate R-function. We obtain Geraghty fixed point theorem [ ], if the function λ ∈ is defined by λ(u) = for all u ∈ Z.

If u and v

Conclusions