THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Ayse T. Bugatekin

,

Gökhan Gökdere

THE APPLICATION OF BERNOULLI TRIALS TO THE THEORY OF APPROXIMATION

ABSTRACT
In recent years, q-Bernstein polynomials and α-Bernstein polynomials have emerged as prominent topics in approximation theory. Numerous studies have examined the convergence criteria of these polynomials, highlighting their importance and usefulness. The main idea underlying the article is that the kernels of these polynomials depend on the probabilities of the variable parameter binomial distribution. Taking advantage of this property, we developed a simplified form of these polynomials regarding binomial dependence. This facilitated the calculation of moments for a binomial variable with variable parameters. This method both simplifies the computational processes and allows us to better understand the convergence properties of these polynomials. By examining these reduced forms, important information has been obtained regarding the structure of the underlying distribution. The findings underscore the versatility and power of q-Bernstein and α-Bernstein polynomials in approximation theory and provide a deeper understanding of their mathematical foundations and potential applications.
KEYWORDS
approximation theory, Bernstein polynomial, Bernoulli process, convergence, expected values
PAPER SUBMITTED: 2024-07-02
PAPER REVISED: 2024-10-14
PAPER ACCEPTED: 2024-11-01
PUBLISHED ONLINE: 2025-01-25
DOI REFERENCE: https://doi.org/10.2298/TSCI2406991B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2024, VOLUME 28, ISSUE Issue 6, PAGES [4991 - 4999]
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The application of Bernoulli trials to the theory of approximation

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence