On Hermite type sampling Kantorovich operators in the settings of mixed norm Spaces

TL;DR

This paper studies the convergence and approximation properties of Hermite-type sampling Kantorovich operators within mixed norm spaces, providing theoretical results and practical implementation insights using cardinal B-splines.

Contribution

It introduces new convergence theorems and approximation estimates for these operators in mixed norm spaces, including error bounds and asymptotic formulas.

Findings

Proved uniform convergence and asymptotic formulas.

Estimated the rate of convergence via modulus of continuity.

Demonstrated implementation using cardinal B-splines.

Abstract

In this paper, we analyze the convergence behavior of Hermite-type sampling Kantorovich operators in the context of mixed norm spaces. We prove certain direct approximation theorems, including the uniform convergence theorem, the Voronovskaja-type asymptotic formula, and an estimate of error in the approximation in terms of the modulus of continuity in mixed norm settings. Next, we estimate the rate of convergence of these sampling Kantorovich operators in terms of the modulus of continuity. In addition, we obtain simultaneous approximation results of these sampling Kantorovich operators, including the uniform approximation, the asymptotic formula, and the approximation error in terms of the modulus of continuity in mixed settings. Finally, using cardinal $B$-splines, the implementation of differentiable functions has been shown.