Elsevier

Topology and its Applications

Volume 156, Issue 17, 1 November 2009, Pages 2838-2844
Topology and its Applications

Monotone generalized contractions in partially ordered probabilistic metric spaces

Dedicated to S.M. Vaezpour
https://doi.org/10.1016/j.topol.2009.08.029Get rights and content
Under an Elsevier user license
open archive

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.

MSC

primary
54H25
secondary
47H10

Keywords

Non-decreasing mapping
Coincidence
Fixed point
Common fixed point
Complete metric space complete

Cited by (0)