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

Andi Kivinukk; Anna Saksa

doi:10.3934/mfc.2021030

Article Contents

2022, Volume 5, Issue 3: 197-218. Doi: 10.3934/mfc.2021030

This issue Previous Article Convergence of modified Szász-Mirakyan-Durrmeyer operators depending on certain parameters Next Article Boundedness properties of semi-discrete sampling operators in Mellin–Lebesgue spaces

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

Andi Kivinukk^1, , and
Anna Saksa^2,

1.
Tallinn University, Narva Str. 25, 10120 Tallinn, Estonia
2.
Estonian Maritime Academy, Tallinn Univ. of Technology, Kopli 101, 11712 Tallinn, Estonia

^* Corresponding author: A. Kivinukk
^* Corresponding author: A. Kivinukk

Received: May 31, 2021

Revised: August 31, 2021

Early access: November 2021

Published: August 2022

Research supported partially by the EU, European Reg. Develop. Fund ASTRA project for 2016-2022 of Estonian Doctoral School in Mathematics and Statistics; Tallinn University TLU TEE

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Abstract

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.

Keywords:

Cosine operator function,
Rogosinski-type approximation processes,
modulus of continuity,
degree of approximation.

Mathematics Subject Classification: Primary: 41A65; Secondary: 41A17.

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