Linear Approximation Processes Based on Binomial Polynomials

Octavian Agratini () and Maria Crăciun
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Octavian Agratini: Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, 57 Fântânele Street, 400320 Cluj-Napoca, Romania
Maria Crăciun: Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, 57 Fântânele Street, 400320 Cluj-Napoca, Romania

Mathematics, 2025, vol. 13, issue 15, 1-25

Abstract: The purpose of the article is to highlight the role of binomial polynomials in the construction of classes of positive linear approximation sequences on Banach spaces. Our results aim to introduce and study an integral extension in Kantorovich sense of these binomial operators, which are useful in approximating signals in L p ( [ 0 , 1 ] ) spaces, p ≥ 1 . Also, inspired by the coincidence index that appears in the definition of entropy, a general class of discrete operators related to the squared fundamental basis functions is under study. The fundamental tools used in error evaluation are the smoothness moduli and Peetre’s K-functionals. In a distinct section, numerical applications are presented and analyzed.

Keywords: binomial polynomial; umbral calculus; linear positive operator; r-modulus of smoothness; Peetre’s K-functionals; Kantorovich-type operator; Hardy–Littlewood maximal operator; index of coincidence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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