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On the existence and uniqueness problems of solutions for set-valued and single-valued nonlinear operator equations in probabilistic normed spaces. (English) Zbl 0801.47043

Following Altman’s theory of contractors on normed spaces [M. Altman, Contractors and contractor directions. Theory and applications. A new approach to solving equations. Lecture Notes in Pure and Applied Mathematics, Vol. 32 (1977; Zbl 0363.65045)] the authors study contractors and fixed points on Menger probabilistic normed spaces.

MSC:

47H10 Fixed-point theorems
47S50 Operator theory in probabilistic metric linear spaces
47H04 Set-valued operators
54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology
54E70 Probabilistic metric spaces

Citations:

Zbl 0363.65045
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