Convergence in distribution of the Bernstein-Durrmeyer kernel and pointwise convergence of a generalised operator for functions of bounded variation

2023/03/20 by Mohammed Taariq Mowzer, Mowzer, Mohammed Taariq
Engineering · Mathematics · #41A81 (Primary) 41A10 #60F05 (Secondary) #Advanced Numerical Analysis Techniques #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2303.11061

openalex publication_date 2023/03/20 · openalex created_date 2023/03/23 · openalex updated_date 2026/07/28

Abstract

We study the convergence of Bernstein type operators leading to two results. The first: The kernel K_n of the Bernstein-Durrmeyer operator at each point x ∈ (0, 1) \unicodex2013 that is K_n(x, t) dt \unicodex2013 once standardised converges to the normal distribution. The second result computes the pointwise limit of a generalised Bernstein-Durrmeyer operator applied to \unicodex2013 possibly discontinuous \unicodex2013 functions f of bounded variation.

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