On Rogosinski-type approximation processes in Banach space using the framework of the cosine operator function

Abstract

<p style='text-indent:20px;'>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.</p>