Related papers: A note on comparison between Birkhoff and McShane-…
In this work we construct logarithms and Birkhoff normal forms for elliptic Fourier integral operators in the semi-classical limit under more general assumptions than in aprevious work by the first author. The methods are similar but…
A bi-univalent function is a univalent function defined on the unit disk with its inverse also univalent on the unit disk. Estimates for the initial coefficients are obtained for bi-univalent functions belonging to certain classes defined…
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…
A multivalued integral in Riesz spaces is given using the Kurzweil-Henstock integral construction. Some of its properties and a comparison with the Aumann approach are also investigated.
We obtain integral representations of the $n$-th derivatives of the Bessel functions with respect to the order. The numerical evaluation of these expressions is very efficient using a double exponential integration strategy. Also, from the…
In this paper, we first prove two new identities for multiplicative differentiable functions. Based on this identity, we establish a midpoint and trapezoid type inequalities for multiplicatively convex functions. Applications to special…
We give an introduction to a theory of b-functions, i.e. Bernstein-Sato polynomials. After reviewing some facts from D-modules, we introduce b-functions including the one for arbitrary ideals of the structure sheaf. We explain the relation…
In this paper, we establish some integral ineuqalities for n- times differentiable quasi-convex functions.
The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{D}^n$.We also prove two other sharp versions of the Bohr inequality in the setting…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by means of related Riemann integrals. In particular, we…
We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.
In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the…
Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we…
In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex functions over rectifiable hyperbolic path. Also we have established…
In this paper we extend the concept of bi-univalent to the class of meromorphic functions. We propose to investigate the coefficient estimates for two classes of meromorphic bi-univalent functions. Also, we find estimates on the…
In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind and express it in terms of the Lerch function. There are some useful results relating double…
In this paper we consider a new kind of inequality related to fractional integration, motivated by Gressman's paper. Based on it we investigate its multilinear analogue inequalities. Combining with the Gressman's work on multilinear…