Eurasian Mathematical Journal

Approximation by T means with respect to Vilenkin system in Lebesgue spaces

Nino Anakidze — 2025-12-23

In this paper we present and prove some new results concerning approximation properties of \(T\) means with respect to the Vilenkin system in Lebesgue spaces for any \(1 \le p < \infty\). As applications, we obtain extensions of some known approximation inequalities.

Boundedness of the generalized Riemann–Liouville operator in local Morrey-type spaces with mixed quasi-norms

Victor Burenkov — 2025-12-23

The objective of this paper is to establish sufficient conditions for the boundedness of the generalized Riemann–Liouville operator in local Morrey-type spaces with mixed quasi-norms on a parallelepiped and to obtain sharp estimates of the norm of this operator with respect to the lengths of the edges of this parallelepiped.

Infinitely many periodic solutions for differential equations involving piecewise alternately advanced and retarded argument

Kuo-Shou Chiu — 2025-12-23

The manuscript introduces an innovative framework for establishing the existence of infinitely many nontrivial periodic solutions within a class of differential equations characterized by a piecewise alternately advanced and retarded argument. It comprehensively delineates the essential criteria required for the existence of these solutions and provides detailed procedures for their determination. Additionally, the study incorporates illustrative examples, including cases with infinitely many solutions, to demonstrate the effectiveness and applicability of the proposed approach.

Propagation of nonsmooth waves along a star graph with fixed boundary vertices

Baltabek Kanguzhin — 2025-12-23

The paper studies the spread of waves along a star graph. The continuation of the initial data from the graph edges for the entire numerical axis allows one to represent an analogue of the d’Alembert formula for waves on the star graph. At the same time, the continuation of the initial data is closely related to the continuation of the system of its eigenfunctions of the Sturm–Liouville problem originally defined on the star graph. The continuation of the eigenfunctions defined on the star graph is based on the continuation of the initial data of the mixed problem for the wave equation. The indicated continuation of the initial data of the mixed problem was proposed by B. M. Levitan.

Continuous extension to the boundary of a domain of the logarithmic double layer potential

Serhiy Anatoliyovych Plaksa — 2025-12-23

For the real part of the Cauchy-type integral that is known to be the logarithmic potential of the double layer, a necessary and sufficient condition for the continuous extension to the Ahlfors-regular boundary is established. Sufficient conditions involving subclasses of Ahlfors-regular curves are also considered. Illustrative examples are presented.

Sonin’s inventory model with a long-run average cost functional

Ernst L. Presman — 2025-12-23

We present an inventory model where a manufacturer (firm) uses for “production” a “commodity” (resource), which is consumed with the unit intensity. The price of the commodity follows a stochastic process, modelled by a continuous-time Markov chain with a finite number of states and known transition rates. The firm can buy this commodity at the current price or use a “stored” one. The storage cost is proportional to the storage level. The goal of the firm is to minimize the long-run average cost functional.

We prove the existence of a canonical triplet with an optimal threshold strategy, present an algorithm for constructing optimal thresholds and the optimal value of the functional, and discuss issues of uniqueness.