Some common random fixed point theorems for contractive type conditions in cone random metric spaces

Abstract

Abstract. In this paper, we establish some common random fixed point theorems for contractive type conditions in the setting of cone random metric spaces. Our results unify, extend and generalize many known results from the current existing literature.

Random Fixed Point Theorem for Weakly Compatible Mappings under Implicit Relation in Cone Random Metric Spaces

“…Letting P = Q = I (where I is the identity mapping defined by I(ω, x) = x(ω) for all ω ∈ Ω) and eliminating the conditions (i) ,(ii) in our theorem, we obtain the results of Saluja and Tripathi [28].…”

“…Random fixed point results in cone random metric spaces are stochastic generalization of deterministic fixed point results in cone metric space. Several other authors see [15,22,[26][27][28][29] studied the existence of random fixed points and common random fixed points of mappings satisfying contractive type conditions in setting cone random metric spaces.…”

“…In continuation of these results, we extend the contraction condition via implicit relation by Saluja and Tripathi [28] to four random operators and obtain a common random fixed point for four weakly compatible mappings on a nonempty separable closed subset of cone random metric spaces. [16] Let (E, τ ) be a topological vector space.…”

Common random fixed point results with application to a system of nonlinear integral equations

“…Common random fixed points and random coincidence points of a pair of compatible random operators and fixed point theorems for contractive random operators in Polish spaces are obtained by Papageorgiou [13], [14] and Beg [2], [3]. Subsequently Saluja and Tripathi [23] obtained the stochastic version of the result of Mehta et al [16].…”

Results on Generalized Quasi Contraction Random Operators

“…Saluj [15] establish some common random fixed point theorems under contractive type condition in the framework of cone random metric spaces. Rashwan and Albaqeri [16] obtained common random fixed point theorems for six weakly compatible random operators defined on a nonempty closed subset of a separable Hilbert space.…”