Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences最新文献

Abstract

In the work the almost everywhere (a.e.) convergence (absolute convergence) of series by the general Haar and Franklin systems corresponding to weakly regular division of the segment ([0,1]) are compared. It is proved that if a series by the general Haar system diverges (absolutely diverges) on a set (E), then the series by the general Franklin system with the same coefficients diverges (absolutely diverges) a.e. in (E). As a consequence, it is obtained that if a sequence (omega_{n}) is not a Weyl multiplier for unconditional a.e. convergence of series by the general Haar system, then it is not a Weyl multiplier for unconditional a.e. convergence of series by the general Franklin series.

Abstract

Erdös–Lax inequality relates the sup norm of the derivative of a polynomial along the unit circle to that of the polynomial itself (on the unit circle). This paper aims to extend the classical Erdös–Lax inequality to the polar derivative of a polynomial by using the extreme coefficients of the given polynomial. The obtained results not only enrich the realm of Erdös–Lax-type inequalities but also offer a promising avenue for diverse applications where these inequalities play a pivotal role. To illustrate the practical significance of our results, we present a numerical example. It vividly demonstrates that our bounds are considerably sharper than the existing ones in the extensive literature on this captivating subject.

Abstract

The paper provides a classification of nontrivial dual hyperidentities of the left and right distributivity satisfied in functionally nontrivial divisible algebras. If the nontrivial dual hyperidentities of the left and right distributivity hold in a functionally nontrivial divisible algebra, then the hyperidentity of the left distributivity is of rank two and is (equivalent to the hyperidentity) of the form

while the hyperidentity of the right distributivity is the hyperidentity of rank two and is (equivalent to the hyperidentity) of the form

For the classification of nontrivial hyperidentities of the left and right distributivity satisfying in functionally nontrivial (q)-algebras, see [1–4].

Abstract

An infinite system of integral equations with power nonlinearity on the positive half-line is considered. A number of particular cases of this system arise in many branches of mathematical physics. In particular, systems of this nature are encountered in the theory of radiative transfer in spectral lines, in the dynamic theory of (p)-adic open-closed strings, in the mathematical theory of the spread of epidemic diseases, and in econometrics. The existence of a nonnegative (in coordinates) nontrivial and bounded solution is proved. Under an additional constraint on the matrix kernel, we also study the asymptotic behavior at infinity. In the case of strong symmetry (symmetry both in coordinates and in indices) of the matrix kernel, we also prove a uniqueness theorem for a solution in a certain class of infinite and bounded vector functions. At the end, concrete examples of an infinite matrix kernel are given that are of practical interest in the above applications.

Abstract

We give a geometric characterization of knot sequences ((s_{n})), which is a necessary condition for the corresponding periodic orthonormal spline system of arbitrary order (k), (kinmathbb{N}), to be an unconditional basis in the atomic Hardy space on the torus (H^{1}(mathbb{T})).

Abstract

In the present paper, we consider a subclass of starlike functions (mathcal{G}_{mu}) introduced by Silverman. It is defined by the ratio of analytic representations of convex and starlike functions. The main aim is to determine the sharp bounds of coefficient problems for the inverse of functions in this class. We derive the upper bounds of some initial coefficients, the Fekete–Szegö type inequality and the second Hankel determinant (mathcal{H}_{2,2}left(f^{-1}right)) for (finmathcal{G}_{mu}). On the third Hankel determinant (mathcal{H}_{3,1}left(f^{-1}right)), we give a bound on the inverse of (finmathcal{G}). All the results are proved to be sharp.

Abstract

In the paper, the sufficient conditions are found for the convergence, summability by the Cesàro methods and unconditional convergence almost everywhere of orthogonal series, which are equivalent to the well-known theorems of Menshov–Redemacher, Menshov, and Orlich.

Abstract

In the paper we give direct theorems on approximation by Haar and Walsh polynomials in weighted generalized grand Lebesgue space. Also the degree of approximation by Borel, Euler, Riesz–Zygmund, and Nörlund linear means of Walsh–Paley–Fourier series are treated in the above cited space.

Abstract

In this paper, we study the existence of meromorphic solutions of hyperorder strictly less than 1 to the Fermat-type differential-difference equations, which improves earlier results of such studies.

Abstract

We give a geometric characterization of knot sequences ((s_{n})), which is a sufficient condition for the corresponding periodic orthonormal spline system of arbitrary order (k), (kinmathbb{N}), is an unconditional basis in the atomic Hardy space on the torus (H^{1}(mathbb{T})).