Revisiting Kantorovich Operators in Lebesgue Spaces
Maximillian Ventura Obie,
Erick Angga Taebenu,
Reinhart Gunadi
et al.
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 o… Show more
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