Work

On the Application of Analogues of the Korovkin Theorem to the Convergence of Certain Classes of Sequences of Convolution Operators

Year: 2025

Type: article

Abstract: This paper establishes conditions on the Young function Φ and the summability exponent p(•) that ensure the validity of analogues of Korovkin's theorem for sequences of positive convolution operators in Orlicz spaces L Φ and Lebesgue spaces L p (•) with a variable summability exponent.The results obtained in the space L Φ are applied to the convergence of a sequence of Fejer and Poisson operators.Also, using the obtained result, the convergence of the family of Fejer and Steklov operators to the unit operator in the space L p (•) is established.

Source: Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan

DOI: 10.30546/2409-4994.2025.51.1.1027

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4410849552

FWCI:

Cites: 3

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Related to: 10