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Denny Ivanal Hakim
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Chemistry Control & Systems Engineering Engineering Mathematics Physics

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Journal : hilbert journal of mathematical analysis

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Rate of convergence of Kantorovich operator sequences near L1([0, 1]) Abdul Karim Munir Aszari; Denny Ivanal Hakim
Hilbert Journal of Mathematical Analysis Vol. 3 No. 1 (2024): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v3i1.37

Abstract

The study of the rate of convergence of Kantorovich operator sequences has predominantly focused on the Lp spaces for 1< p<infty, yet the behaviour near L1([0,1]) remains less understood, particularly as p approaches 1. To bridge this gap, we investigate the rate of convergence within the framework of the grand Lebesgue spaces Lp ([0,1]), which encompass all Lp ([0,1]) spaces for 1<p<infty but remain a subset of L1([0,1]). Our approach leverages the intrinsic properties of Lp ([0,1]) to derive new results on the convergence rate of Kantorovich operator sequences. Specifically, our objective is to demonstrate that Kantorovich operators exhibit a significant rate of convergence within this broader context, thereby providing insights applicable to the boundary behavior as p to 1. We will then apply these findings to alpha-Holder continuous functions to further understand the convergence rate of Kantorovich operator sequences in these settings. This combined approach suggests that functions with derivatives in Lp ([0,1]) exhibit specific convergence rates under Kantorovich operators.
Co-Authors Abdul Karim Munir Aszari