C&SA | Contents

Volume 61 >>> № 6 NOVEMBER — DECEMBER 2025

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UDC 519.8

D.V. Shapovalov
Lesya Ukrainka Volyn National University, Lutsk, Ukraine,
shapovalovdv@ukr.net

A.M. Shutovskyi
Lesya Ukrainka Volyn National University, Lutsk, Ukraine,
sh93ar@gmail.com

ASYMPTOTIC PROPERTIES OF A CERTAIN SYSTEM
OF ORTHOGONAL POLYNOMIALS

Abstract. The paper formulates and solves an optimization problem concerning the study of the deviation of the Lipschitz class functions from the superposition of orthogonal polynomials. The problem is based on a positive operator as a generalization of the Abel–Poisson integral and the biharmonic Poisson integral. The main result of the research is presented in the form of an asymptotic equality for the deviation of Lipschitz functions from the constructed generalized Poisson-type operator. The applicability of the operator under consideration in the optimal decision theory is determined by its belonging to the class of positive operators as optimal solutions to boundary value problems. In addition, the optimality of the generalized Poisson-type operator is significantly enhanced by the presence of approximation properties for the Lipschitz class functions, which can act as mathematical models in optimal design problems.

Keywords: Lipschitz class functions, optimization problem, asymptotic equality, generalized operator.

full text

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UDC 519.8

ASYMPTOTIC PROPERTIES OF A CERTAIN SYSTEM OF ORTHOGONAL POLYNOMIALS

REFERENCES

ASYMPTOTIC PROPERTIES OF A CERTAIN SYSTEM
OF ORTHOGONAL POLYNOMIALS