TY  - JOUR
T1  - A New Generalization of Szász-Mirakjan Kantorovich Operators for Better Error Estimation
AU  - Baytunç, Erdem
AU  - Aktuğlu, Hüseyin
AU  - Mahmudov, Nazım
PY  - 2023
DA  - December
Y2  - 2023
DO  - 10.33401/fujma.1355254
JF  - Fundamental Journal of Mathematics and Applications
JO  - Fundam. J. Math. Appl.
PB  - Fuat USTA
WT  - DergiPark
SN  - 2645-8845
SP  - 194
EP  - 210
VL  - 6
IS  - 4
LA  - en
AB  - 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.
KW  - Affine functions
KW  - Bivariate
Szasz-Mirakjan Kantorovich operators
KW  - ´
Modulus of continuity
KW  - Positive Linear
Operators
KW  - Rate of convergence
KW  - Szasz- ´
Mirakjan Kantorovich operator
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UR  - https://doi.org/10.33401/fujma.1355254
L1  - https://dergipark.org.tr/en/download/article-file/3385618
ER  -