Quantitative estimates for wavelet type extension of generalized Kantorovich operators

Year 2025, Volume: 8 Issue: Special Issue: ICCMA, 39 - 48, 16.12.2025

Gülen Başcanbaz- Tunca , Ayşegül Erençin , Ayşe Feza Güvenilir

https://doi.org/10.33205/cma.1784422

Abstract

In this paper, we consider a sequence of operators as a wavelet type extension of univariate generalized Kantorovich operators depending on a positive real parameter given in [3]. We establish quantitative estimates for the rate of convergence of these operators in the continuous functions space and $L^{p}$-spaces in terms of modulus of continuity and $K$-functionals, respectively. Furthermore, some inequalities such as Bernstein-Markov type for continuous functions and variation preservation type property of the operators when the involved function is of bounded variation are provided.

Keywords

Generalized Kantorovich operators , wavelets , modulus of continuity , K-functionals , Bernstein-Markov type inequality , Hardy-Littlewood maximal function

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