# American Institute of Mathematical Sciences

February  2020, 25(2): 733-747. doi: 10.3934/dcdsb.2019264

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

 Babeş-Bolyai University, Department of Mathematics, 400084 Cluj-Napoca, Romania

Dedicated to Professor Juan J. Nieto on the occasion of his 60th birthday

Received  November 2018 Revised  January 2019 Published  November 2019

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.

Citation: Adrian Petruşel, Radu Precup, Marcel-Adrian Şerban. On the approximation of fixed points for non-self mappings on metric spaces. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 733-747. doi: 10.3934/dcdsb.2019264
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