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

Authors : Erdem Baytunç, Hüseyin Aktuğlu, Nazım Mahmudov

Pages : 194-210

Doi:10.33401/fujma.1355254

View : 63 | Download : 85

Publication Date : 2023-12-31

Article Type : Research

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