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Obie, Maximillian Ventura
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Mathematics

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Revisiting Kantorovich Operators in Lebesgue Spaces Obie, Maximillian Ventura; Taebenu, Erick Angga; Gunadi, Reinhart; Hakim, Denny Ivanal
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 3 (NOVEMBER 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.3.1596.289-298

Abstract

According to the Weierstrass Approximation Theorem, any continuous function on the closed and bounded interval can be approximated by polynomials. A constructive proof of this theorem uses the so-called Bernstein polynomials. For the approximation of integrable functions, we may consider Kantorovich operators as certain modifications for Bernstein polynomials. In this paper, we investigate the behaviour of Kantorovich operators in Lebesgue spaces. We first give an alternative proof of the uniform boundedness of Kantorovich operators in Lebesgue spaces by using the Riesz-Thorin Interpolation Theorem. In addition, we examine the convergence of Kantorovich operators in the space of essentially bounded functions. We also give an example related to the rate of convergence of Kantorovich operators in a subspace of Lebesgue spaces.
Co-Authors Gunadi, Reinhart Hakim, Denny Ivanal Taebenu, Erick Angga