Approximation in Weighted Orlicz Spaces with a generating Young function that might be non-convex

Abstract

The aim of this paper is to investigate the order of approximation by some linear summation methods of trigonometric Fourier series in weighted Orlicz spaces which have generating Young functions not necessary to be convex. Obtained estimations base on the fractional modulus of smoothness and the best approximation. Furthermore, a convolution type operator is defined and its estimation by the best approximation is obtained.

Keywords

• Linear summation processes
• Fourier series
• trigonometric approximation
• weighted Orlicz spaces
• Muckenhoupt weight

Konveks olması gerekmeyen genelleştirilmiş Young fonksiyonu ile üretilen Ağırlıklı Orlicz Uzaylarında yaklaşım

Abstract

Bu çalışmada, konveks olması gerekmeyen Young fonksiyonları ile üretilen ağırlıklı Orlicz uzaylarında trigonometrik Fourier serilerinin bazı lineer toplam metodları ile yaklaşım problemleri incelenmiştir. Elde edilen sonuçlar kesirli düzgünlük modülüne ve en iyi yaklaşım sayısına dayanmaktadır. Ayrıca, konvolüsyon tipli dönüşüm tanımlayıp, bu dönüşüm ile en iyi yaklaşım sayısı arasındaki ilişki değerlendirilmiştir.

Keywords

• Lineer toplam metodları
• Fourier serileri
• , trigonometrik yaklaşım
• ağırlıklı Orlicz uzayları
• Muckenhoupt ağırlık fonksiyonu

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