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Probabilistic \(b\)-metric spaces and nonlinear contractions. (English) Zbl 1381.54036
Summary: This work is for giving the probabilistic aspect to the known \(b\)-metric spaces [S. Czerwik, Atti Semin. Mat. Fis. Univ. Modena 46, No. 2, 263–276 (1998; Zbl 0920.47050)], which leads to studying the fixed point property for nonlinear contractions in this new class of spaces.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54E70 Probabilistic metric spaces
47S50 Operator theory in probabilistic metric linear spaces
34B15 Nonlinear boundary value problems for ordinary differential equations
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