A New Generalization of Szász-Mirakjan Kantorovich Operators for Better Error Estimation

Year 2023, Volume: 6 Issue: 4, 194 - 210, 31.12.2023

Erdem Baytunç , Hüseyin Aktuğlu , Nazım Mahmudov

https://doi.org/10.33401/fujma.1355254

Cited By: 4

Abstract

In this article, we construct a new sequence of Szász-Mirakjan-Kantorovich operators denoted as $K_{n,\gamma}(f;x)$, which depending on a parameter $\gamma$. We prove direct and local approximation properties of $K_{n,\gamma}(f;x)$. We obtain that, if $\gamma>1$, then the operators $K_{n,\gamma}(f;x)$ provide better approximation results than classical case for all $x\in[0,\infty)$. Furthermore, we investigate the approximation results of $K_{n,\gamma}(f;x)$, graphically and numerically. Moreover, we introduce new operators from $K_{n,\gamma}(f;x)$ that preserve affine functions and bivariate case of $K_{n,\gamma}(f;x)$. Then, we study their approximation properties and also illustrate the convergence of these operators comparing with their classical cases.

Keywords

Affine functions, Bivariate Szasz-Mirakjan Kantorovich operators, ´ Modulus of continuity, Positive Linear Operators, Rate of convergence, Szasz- ´ Mirakjan Kantorovich operator

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