Parçalı Bir Fonksiyonla Tanımlı Bernstein Stancu Operatörleri

Yıl 2025, Cilt: 15 Sayı: 2, 184 - 216, 31.12.2025

Emine Güven , Nazmiye Gönül Bilgin

https://doi.org/10.37094/adyujsci.1660367

Öz

Bu çalışmada Stancu tipi operatörlerin parametreye bağlı iki farklı genelleştirmesinin yaklaşım özellikleri incelenmiştir. İlk aşamada, [-1,1] aralığında tanımlı bu operatörün teoremi sağlayan Korovkin tipi bir operatör olduğu belirlenmiş ve önemli özellikleri incelenmiştir. Daha sonra, bu operatör kullanılarak Kantorovich tipi yeni bir operatör sınıfı tanımlanmış ve bu operatörlerin yaklaşım özellikleri üzerine çalışılmıştır. Çalışmanın bir diğer önemli kısmı ise her iki sınıf operatörün Lp uzaylarında yakınsaklık özelliklerinin incelenmesidir. Bu bağlamda, operatörlerin fonksiyonlar üzerindeki etkisi ve yakınsaklık özellikleri değerlendirilmiş ve yeni tanımlanan operatörlerin klasik yaklaşımlara göre avantajları gösterilmiştir. Ayrıca, bu operatörlerin yaklaşım grafikleri sunulmuş ve operatörlerin fonksiyonlar üzerindeki etkileri görsel olarak analiz edilmiştir. Çalışma, her iki operatörün teorik analizini ve görsel sonuçlarını sunarak, yakınsamaları hakkında önemli bilgiler sağlamaktadır.

Anahtar Kelimeler

Bernstein Stancu Operatörleri , Korovkin Teoremi , Kantorovich Operatörleri

Stancu and Kantorovich-Type Generalizations of a Bernstein Operator: Approximating Locally Integrable Functions

Öz

This study investigates the approximation properties of two different types of parameter-dependent generalizations of Stancu type operators. In the first step, it is determined that this operator defined on the interval [-1,1] is an operator of Korovkin type satisfying the theorem and its important properties are analyzed. Then, a new class of operators of Kantorovich type is defined using this operator and the study on the approximation properties of these operators is elaborated. Another important part of the study is to investigate the convergence properties of both classes of operators in Lp spaces. In this context, the effect of the operators on functions and their convergence properties are evaluated and the advantages of the newly defined operators over the classical approximations are demonstrated. In addition, graphs of the approximation of these operators are presented and the effects of the operators on the functions are visually analyzed. By presenting the theoretical analysis and visual results of both operators, the study provides important information about their convergence.

Anahtar Kelimeler

Bernstein Stancu Operators , Kantorovich Operators , Korovkin's Theorem

Kaynakça

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