We express the generalized Cauchy-Stieltjes transforms of some particular Beta distributions depending on a positive parameter λ as λ-powered Cauchy-Stieltjes transforms of some probability measures. The Cauchy-Stieltjes transforms of the latter measures are shown to be the geometric mean of the Cauchy-Stieltjes transform of the Wigner law together with another one. Moreover, they are absolutel...

A completion functor is constructed on the category of completely normal Cauchy groups and Cauchy-continuous homomorphlsms. A competlon functor is also obtained for a corresponding category of convergence groups.

In this paper, we introduce the concepts of I2-Cauchy, I∗ 2 -Cauchy double sequence of fuzzy numbers and study their some properties and relations, where I2 denotes the ideal of subsets of N× N.

We use a fixed point method to prove the Cauchy–Rassias stability of homomorphisms associated to the Pexiderized Cauchy–Jensen type functional equation r f ( x+ y r ) + sg ( x− y s ) = 2h(x), r,s ∈ R\{0}

We prove that the obstacle problem for a non-uniformly parabolic operator of Kolmogorov type, with Cauchy (or Cauchy-Dirichlet) boundary conditions, has a unique strong solution u. We also show that u is a solution in the viscosity sense.

Ateya and Madhagi (2011) introduced a multivariate form of truncated generalized Cauchy distribution (TGCD), which introduced by Ateya and Al-Hussaini (2007). The multivariate version of (TGCD) is denoted by (MVTGCD). Among the features of this form are that subvectors and conditional subvectors of random vectors, distributed according to this distribution, have the same form of distribution ...