# Some fixed point results linked to α –β rational contractions and modified multivalued Hardy-Rogers operators

## Abstract

In this paper two new fixed point results are studied. The first result is a theorem that involves (α −β) type rational singlevalued contractions, in the sense of Geraghty type operators. The second result consists of multivalued modified Hardy Rogers operators, namely the existence of the fixed point, data dependence, local version involving two metrics and homotopy theorems involving two metrics are studied.

## Authors

Cristian Daniel Alecsa
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania

## Keywords

fixed point theorems; complete metric space; rational contractions; multivalued; homotopy; Geraghty;
Hardy-Rogers.

## Paper coordinates

C.-D. Alecsa, Some fixed point results linked to α –β rational contractions and modified multivalued Hardy-Rogers operators, J. Fixed Point Theory, 2018, 2018:3.

## PDF

##### Journal

J. Fixed Point Theory

2052-5338

2052-5338