Coupled fixed points of mixed monotone operators on probabilistic Banach spaces. (English) Zbl 1068.47093

Beg, Ismat; Latif, Abdul; Ali, Rashid; Azam, Akbar

Arch. Math., Brno 37, No. 1, 1-8 (2001).

Four theorems concerning the existence of coupled fixed points to monotone operators in probabilistic Banach spaces are presented. Fixed points are furthermore specified to be minimal and maximal. The construction of these fixed points is indicated as well. The technique relies on the notion of probabilistic Kuratowski’s measure of noncompactness.

Reviewer: Jan Andres (Olomouc)

MSC:

47S50	Operator theory in probabilistic metric linear spaces
47H10	Fixed-point theorems
47H05	Monotone operators and generalizations

Keywords:

monotone operators; probabilistic space; coupled fixed points