Vol 52, No 6 (2017)
- Year: 2017
- Articles: 6
- URL: https://journals.rcsi.science/1068-3623/issue/view/14077
Differential Equations
Existence of solutions for discrete fractional difference inclusions with boundary conditions
Abstract
This paper is mainly concerned with the existence of solutions for a certain class of discrete fractional difference inclusions with boundary conditions.Under certain suitable conditions, the existence results are established by using fixed point theory for multi-valued upper semicontinuous maps. Also, an example is presented to illustrate the possible applications of the obtained results.
Functional Analysis
An integral representation and embedding theorems in the plane for multianisotropic spaces
Abstract
The present paper is a continuation of the author’s paper [1], where by means of a special integral representation of functions we prove embedding theorems for multianisotropic functional spaces. In contrast to [1], here we consider the case where the corresponding completely regular polyhedron has many anisotropy vertices.
Extended Srivastava’s triple hypergeometric HA,p,q function and related bounding inequalities
Abstract
In this paper, motivated by certain recent extensions of the Euler’s beta, Gauss’ hypergeometric and confluent hypergeometric functions (see [4]), we extend the Srivastava’s triple hypergeometric function HA by making use of two additional parameters in the integrand. Systematic investigation of its properties including, among others, various integral representations of Euler and Laplace type, Mellin transforms, Laguerre polynomial representation, transformation formulas and a recurrence relation, is presented. Also, by virtue of Luke’s bounds for hypergeometric functions and various bounds upon the Bessel functions appearing in the kernels of the newly established integral representations, we deduce a set of bounding inequalities for the extended Srivastava’s triple hypergeometric function HA,p,q.
Integral Equations
On a transformation of integral equations
Abstract
Let E = E(a, b) be some Banach space of measurable functions on (a, b), I be the identity operator, and let \(\hat K\) be a Fredholm-type regular integral operator acting on E and \({\hat K_ \pm }\) be its triangular parts. We consider the representation \(I - \hat K = \left( {I - {{\hat K}_ - }} \right)\left( {I - \hat U} \right)\left( {I - {{\hat K}_ + }} \right)\), for some known classes of integral operators. In particular,we show that under certain conditions the operator \(\hat U\) is positive and its spectral radius satisfies the condition \(r\left( {\hat U} \right) < 1\). Also, we give some possible applications of the representation.
Real and Complex Analysis
Bounded projectors and duality in the spaces of functions holomorphic in the unit ball
Abstract
The paper studies the Banach spaces h∞(φ), h0(φ), and h1(η) of harmonic functions over the unit ball in Rn. These spaces depend on a weight function φ and a weight measure η. For a given function φ from a sufficiently broad class of functions, we solve the duality problem. that is, we construct measures η such that h1(η)* ∼ h∞(φ) and h0(φ)* ∼ h1(η).
Stochastic and Integral Geometry
Mean covariogram of cylinders and applications to Boolean random sets
Abstract
This work focuses on the variance properties of isotropic Boolean random sets containing randomly-oriented cylinders with circular cross-section. Emphasis is put on cylinders with large aspect ratios, of the oblate and prolate types. A link is established between the power law decay of the covariance function and the variance of the estimates of the volume fraction of cylinders. The covariance and integral range of the Boolean mixtures are expressed in terms of the orientation-averaged covariogram of cylinders, for which exact analytical formulas and approximate expressions are provided.