# Some fixed point results regarding convex contractions of Presić type

## Abstract

In the present paper, we introduce new types of Presić operators. These operators generalize the well-known Istrăţescu mappings, known as convex contractions. Also, we study the existence and uniqueness of fixed points for this type of operators and the convergence of one-step sequence toward the unique fixed point. Also, data dependence results are presented. Finally, some examples are given, suggesting that the above mappings are proper generalizations of convex contractions of second order

## 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

Convex contractions; fixed point; Presic operators; data dependence.

## Paper coordinates

C.-D. Alecsa, Some fixed point results regarding convex contractions of Presić type, J. Fixed Point Theory Appl., 20 (2018), art. 7,
DOI: 10.1007/s11784-018-0488-7

## PDF

##### Journal

Journal of Fixed Point Theory and Applications

Springer

1661-7738