Approximation by a new Schurer type Stancu Operators and Associated GBS

Year 2024, Volume: 14 Issue: 2, 103 - 122, 31.12.2024

Nesibe Manav Mutlu

https://doi.org/10.37094/adyujsci.1484906

Abstract

This study presents a novel extension of the Schurer type Stancu operators and investigates their properties in terms of approximation. The uniform convergence of these operators is provided using the Korovkin Theorem, and the rates of convergence are expressed in terms of the modulus of continuity. Subsequently, the theorem known as Grüss-Voronovskaja is proven. In addition, the related generalized Boolean sum (GBS) operators are defined, and the rates of approximation for these operators are obtained using the mixed modulus of smoothness and functions from the Lipshitz class. Then, numerical examples and graphical results for both operators are presented.

Keywords

Schurer-Stancu operators;, modulus of continuity;, Grüss-Voronovskaja type theorem, GBS operators.

Yeni bir Schurer tipi Stancu Operatörleri ve ilgili GBS Operatörleri ile Yaklaşım

Abstract

Bu çalışma, Schurer tipi Stancu operatörlerinin yeni bir genelleştirmesini sunmakta ve bu operatörlerin yaklaşım özelliklerini incelemektedir. Bu operatörlerin düzgün yakınsaklığı Korovkin Teoremi yardımıyla verilmiş ve yakınsama hızları süreklilik modülü cinsinden ifade edilmiştir. Daha sonra Grüss-Voronovskaja olarak bilinen teorem ispatlanmıştır. Ayrıca, ilgili genelleştirilmiş Boolean toplamı (GBS) operatörleri tanımlanmış ve bu operatörlerin yaklaşım hızları karma düzgünlük modülü ile Lipshitz sınıfından fonksiyonlar kullanılarak elde edilmiştir. Sonrasında, her iki operatör için sayısal örnekler ve grafiksel sonuçlar sunulmuştur.

Keywords

Schurer-Stancu operatörleri, Süreklilik modülü, Grüss-Voronovskaja tipi teorem, GBS operatörleri

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