## 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.

## About this paper

##### Journal

J. Fixed Point Theory

##### Publisher Name

##### DOI

##### Print ISSN

2052-5338

##### Online ISSN

google scholar link

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