In this paper our primary concern is with the establishment of weighted Hardy inequalities in L(Ω) and Rellich inequalities in L(Ω) depending upon the distance to the boundary of domains Ω ⊂ R with a finite diameter D(Ω). Improved constants are presented in most cases.

Szeg˝ o's procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on [−1, 1] is generalized to nonsymmetric measures. It generates the so-called semi-orthogonal functions on the linear space of Laurent polynomials Λ, and leads to a new orthogonality structure in the module Λ × Λ. This structure can be interpreted in terms of a 2 × 2 matrix measure on [−1, 1], a...

This article defines a new operator called the q-Babalola convolution by using quantum calculus and of normalized analytic functions in open unit disk. We then study class bi-univalent defined disk associated with operator. The main results investigation include some upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szego inequalities class. Many applications finds are highlighted c...

One of the most important problems in study geometric function theory is knowing how to obtain sharp bounds coefficients that appear Taylor–Maclaurin series univalent functions. In present investigation, our aim calculate some estimates involving for family convex functions with respect symmetric points and associated a hyperbolic tangent function. These include first four initial coefficients,...

We study the properties of stationary G-chains in terms their generating functions. In particular, we prove an analogue Szeg\H{o} limit theorem for symplectic eigenvalues, derive expression entropy rate quantum Gaussian processes, and distribution eigenvalues truncated block Toeplitz matrices. also introduce a concept numerical range, analogous to that some its basic properties, mainly context ...

In this paper, we define two classes of meromorphic multivalent functions in the punctured disc U*=w∈C:0<|w|<1 by using principle subordination. We investigate a number useful results including subordination results, some connections with certain integral operator, sandwich properties, an inclusion relationship, and Fekete-Szegö inequalities for belonging these classes. Our are connected ...

In this note we present a remark on the paper “On coefficient inequalities for class of holomorphic mappings associated with spirallike in several complex variables” by Y. Lai and Q. Xu [10] published recently journal Results Mathematics. We show that one theorems concerning finite-dimensional space $${{\mathbb {C}}}^n$$ is direct consequence another one, so it does not need an independent proo...

where the coefficients are Legendre symbols, is called the p-th Fekete polynomial. In this paper the size of the Fekete polynomials on subarcs is studied. We prove essentially sharp bounds for the average value of |fp(z)| , 0 < q < ∞, on subarcs of the unit circle even in the cases when the subarc is rather small. Our upper bounds are matching with the lower bounds proved in a preceding paper f...