On the approximation of fixed points for non-self mappings on metric spaces

Abstract

Starting from some classical results of R. Conti, A. Haimovici and K. Iseki, and from a more recent result of S. Reich and A.J. Zaslavski, we present several theorems of approximation of the fixed points for non-self mappings on metric spaces. Both metric and topological conditions are involved. Some of the results are generalized to the multi-valued case. An application is given to a class of implicit first-order differential systems leading to a fixed point problem for the sum of a completely continuous operator and a nonexpansive mapping.

Authors

Adrian Petruşel
Babeş-Bolyai University, Cluj-Napoca, Romania

Radu Precup
Babes-Bolyai University, Cluj-Napoca, Romania

Marcel-Adrian Şerban
Babeş-Bolyai University, Cluj-Napoca, Romania

 

Keywords

Fixed point; metric space; generalized contraction mapping; measure of noncompactness; condensing mapping; nonexpansive mapping;  multi-valued operator; implicit differential equation

Paper coordinates

A. Petruşel, R. Precup, M.-A. Şerban  On the approximation of fixed points for non-self mappings on metric spaces, Discrete and Continuous Dynamical Systems – B, 2020, 25(2): 733-747, https://doi.org/10.3934/dcdsb.2019264

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About this paper

Journal

Discrete and Continuous Dynamical Systems B

Publisher Name

American Institute of Mathematical Sciences

 

Print ISSN

1531-3492

Online ISSN

1553-524X

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