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Probabilistic generalized metric spaces and nonlinear contractions. (English) Zbl 1353.54021
Summary: We give a probabilistic generalization of the theory of generalized metric spaces [A. Branciari, Publ. Math. 57, No.1-2, 31–37 (2000; Zbl 0963.54031)]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff.

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