Modüler Uzaylar Üzerinde Kuvvet Serisi Yöntemine Göre Üçgensel İstatistiksel Göreceli Yakınsaklık ve Korovkin Teorisi

Abstract

Bu makale, üçgensel $P_{p}$-istatistiksel yakınsaklık tanımını ele almaktadır. Ardından üçgensel $P_{p}$-istatistiksel göreceli modüler yakınsaklığı tanıtıyor ve çift indisli diziler için bu yeni yakınsaklığı kullanarak modüler uzaylardaki pozitif lineer operatörler için Korovkin tipi bir yaklaşım teoremi ispatlıyoruz. Ayrıca Orlicz uzaylarındaki moment-tipi operatörlere bir uygulama sunuyor ve geliştirilmiş yaklaşım sonuçları elde ediyoruz. Son olarak, sureklilik modülü yardımıyla yakınsaklık hızı tahminleri veriyoruz.

Keywords

• Üçgensel $P_{p}$-istatistiksel yakınsaklık
• modüler uzaylar
• pozitif lineer operatör
• Korovkin-tipi teorem

Triangular Statistical Relative Convergence with Respect to the Method of Power Series on Modular Spaces and the Theory of Korovkin

Abstract

The present paper deals with the definition of triangular $P_{p}$-statistical convergence. Then we introduce triangular $P_{p}$-statistical relative modular convergence and, using this new convergence for double sequences, we prove an approximation theorem of Korovkin type for positive linear operators in modular spaces. We also present an application to moment-type operators in Orlicz spaces and provide improved approximation results. Finally, we give estimates of the rate of convergence via the modulus of continuity.

Keywords

• Triangular $P_{p}$-statistical convergence
• modular spaces
• positive linear operator
• the Korovkin-type theorem

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