On some fixed point theorems for multi-valued operators by altering distance techique


The aim of this paper is to present some sufficient conditions for the existence and uniqueness of fixed points for (ϕ – ψ) type contractive multi-valued operators defined by altering distances. Furthermore, our main result consists of two theorems, one involving the convergence of the Picard successive approximation sequence to a fixed point of the multivalued ϕ -ψ operator, and a theorem concerning a more general form for a fixed point result for this type of mappings.


Cristian Daniel Alecsa
Babes-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania

Adrian Petrusel
Babes-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania
Academy of Romanian Scientists, Bucharest, Romania


.Fixed point; (ϕ −ψ)-contraction; Altering distance; Multivalued operator; Weakly contractive mapping

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C. D. Alecsa, A. Petrusel, On some fixed point theorems for multi-valued operators by altering distance technique, J. Nonlinear Var. Anal., 1 (2017) no. 2, pp. 237-251.


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J. Nonlinear Var. Anal.

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