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Some random coupled best proximity points for a generalized ω-cyclic contraction in polish spaces

Kongban C., Kumam P.

Fasciculi Mathematici

2017

Nr 59

91--105

In this paper, we will introduce the concepts of a random coupled best proximity point and then we prove the existence of random coupled best proximity points in separable metric spaces. Our results extend the previous work of Akbar et al. [1].

Inner geometry of random operators

Heller M., Pysiak L., Sasin W.

Demonstratio Mathematica

2006

Vol. 39, nr 4

971-978

If V is a foliated manifold, there exists a von Neumann algebra M associated with V. We consider the case when V is a transformation groupoid gamma and the von Neumann algebra M associated with gamma is a noncommutative algebra of random operators. We show that M is generated by a functional algebra A defined on the groupoid gamma with a noncommutative convolution as multiplication, and develop the differential geometry (metric, connection and curvature) based on inner derivations of the algebra A.