1. Monotone generalized contractions in partially ordered probabilistic metric spaces
- Author
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D. Miheţ, Lj. B. Ćirić, and Reza Saadati
- Subjects
Discrete mathematics ,010102 general mathematics ,Fixed-point theorem ,Fixed point ,Fixed-point property ,01 natural sciences ,Coincidence ,Common fixed point ,010101 applied mathematics ,Hausdorff maximal principle ,Metric space ,Complete metric space complete ,Domain theory ,Geometry and Topology ,0101 mathematics ,Total order ,Partially ordered set ,Mathematics ,Non-decreasing mapping - Abstract
In this paper, a concept of monotone generalized contraction in partially ordered probabilistic metric spaces is introduced and some fixed and common fixed point theorems are proved. Presented theorems extend the results in partially ordered metric spaces of Nieto and Rodriguez-Lopez [Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223–239; Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205–2212], Ran and Reurings [A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435–1443] to a more general class of contractive type mappings in partially ordered probabilistic metric spaces and include several recent developments.
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