Open AccessOn Rogosinski-type approximation processes in Banach space using the framework of the cosine operator function
Author(s) -
Andi Kivinukk,
Anna Saksa
Publication year - 2022
Publication title -
mathematical foundations of computing
Language(s) - English
Resource type - Journals
ISSN - 2577-8838
DOI - 10.3934/mfc.2021030
Subject(s) - trigonometric functions , mathematics , approximation property , operator (biology) , type (biology) , banach space , operator theory , function (biology) , trigonometry , pure mathematics , discrete mathematics , mathematical analysis , ecology , biochemistry , chemistry , geometry , repressor , evolutionary biology , biology , transcription factor , gene
In this article, we investigate the approximation properties of general cosine-type operators, especially Rogosinski-type operators, in Banach space when there is a cosine operator function. We apply our approach to both trigonometric Rogosinski operators and Shannon sampling operators. Moreover, for some operators, we derived orders of approximation that include numerical estimates of the constants contained in it. We announced a new direction for approximation issues in the Mellin framework.