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


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.


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



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

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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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Discrete and Continuous Dynamical Systems B

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American Institute of Mathematical Sciences


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