Nonlinear approximation by $N$-dimensional sampling type discrete operators with applications

Year 2024, Volume: 73 Issue: 4, 1134 - 1152

İsmail Aslan

https://doi.org/10.31801/cfsuasmas.1503136

Abstract

In this paper, we explore $N$-dimensional nonlinear discrete operators, closely related to generalized sampling series. We investigate their approximation properties by using the supremum norm and employ a summability method to generalize the discrete operators. The order of convergence is studied by using suitable Lipschitz classes of uniformly continuous functions. We exemplify kernel functions that meet the necessary conditions. Additionally, in the final section of the paper, we propose an operator-based method for digital image zooming.

Keywords

Nonlinear operators, discrete operators, sampling type operators, order of convergence, summability process, digital image processing

Ethical Statement

This study is supported by the Scientific and Technological Research Council of Turkey

Supporting Institution

Scientific and Technological Research Council of Türkiye

Project Number

119F262

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