Approximation on Modular Spaces via P-Statistical Relative A-Summation Process

Abstract

In this paper, we first present the notions of statistical relative modular and F-norm convergence concerning the power series method. Then, we also present theorems of Korovkin-type via statistical relative A-summation process via power series method on modular spaces, including as particular cases weighted spaces, certain interpolation spaces, Orlicz and Musielak-Orlicz spaces, Lp spaces and many others. Later, we consider some application to Kantorovich-type operators in Orlicz spaces. Moreover, we present some estimates of rates of convergence via modulus of continuity. We end the paper with giving some concluding remarks.

Keywords

• Korovkin theorem
• modular space
• statistical convergence
• matrix summability
• power series method

Modüler Uzaylar Üzerinde P-İstatistiksel A-Toplam Süreci Aracılığıyla Yaklaşım

Abstract

Bu çalışmada, ilk olarak, kuvvet serisi yöntemiyle ilgili istatistiksel relative modüler ve F-norm yakınsama kavramlarını sunuyoruz. Daha sonra, özel durumlar olarak ağırlıklı uzaylar, belirli enterpolasyon uzayları, Orlicz ve Musielak-Orlicz uzayları, Lp uzayları ve diğer birçok uzayları içeren modüler uzaylar üzerinde kuvvet serisi yöntemiyle istatistiksel relative A-toplam süreci aracılığıyla Korovkin-tipi teoremleri de sunuyoruz. Daha sonra, Orlicz uzaylarında Kantorovich tipi operatörlere bazı uygulamaları göz önüne alıyoruz. Dahası, süreklilik modülü aracılığıyla yakınsama oranlarının bazı tahminlerini sunuyoruz. Makaleyi bazı son sözler vererek bitiriyoruz.

Keywords

• Korovkin teoremi
• modüler uzay
• istatistiksel yakınsaklık
• matris toplanabilme
• kuvvet serisi yöntemi

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