Approximation by pseudo-linear discrete operators

İsmail Aslan; Türkan Yeliz Gökçer

doi:10.3934/mfc.2021037

Article Contents

2023, Volume 6, Issue 1: 1-13. Doi: 10.3934/mfc.2021037

This issue Previous Article Preface: Special issue on approximation by linear and nonlinear operators with applications. Part III Next Article Analysis of directional higher order jump discontinuities with trigonometric shearlets

Approximation by pseudo-linear discrete operators

İsmail Aslan^1, , and
Türkan Yeliz Gökçer^2,

1.
Hacettepe University, Department of Mathematics, Çankaya, TR-06800, Ankara, Turkey
2.
İstanbul Gedik University, Faculty of Engineering, Department of Computer Engineering, 34876, İstanbul, Turkey

^* Corresponding author: İsmail Aslan
^* Corresponding author: İsmail Aslan

Received: July 2021

Revised: October 2021

Early access: December 2021

Published: February 2023

This study is supported financially by the Scientific and Technological Research Council of Turkey (TÜBÏTAK; project number: 119F262), for which we are thankful.

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Abstract

In this note, we construct a pseudo-linear kind discrete operator based on the continuous and nondecreasing generator function. Then, we obtain an approximation to uniformly continuous functions through this new operator. Furthermore, we calculate the error estimation of this approach with a modulus of continuity based on a generator function. The obtained results are supported by visualizing with an explicit example. Finally, we investigate the relation between discrete operators and generalized sampling series.

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Mathematics Subject Classification: Primary: 41A35, 41A25; Secondary: 41A99.

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Figure 1. Approximation to $ f $ given in (5) by pseudo-linear discrete operators

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