A new type of Szász–Mirakjan operators based on q-integers

Autor: Pembe Sabancigil, Nazim Mahmudov, Gizem Dagbasi
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Journal of Inequalities and Applications, Vol 2023, Iss 1, Pp 1-17 (2023)
Druh dokumentu: article
ISSN: 1029-242X
DOI: 10.1186/s13660-023-03053-6
Popis: Abstract In this article, by using the notion of quantum calculus, we define a new type Szász–Mirakjan operators based on the q-integers. We derive a recurrence formula and calculate the moments Φ n , q ( t m ; x ) $\Phi _{n,q}(t^{m};x)$ for m = 0 , 1 , 2 $m=0,1,2$ and the central moments Φ n , q ( ( t − x ) m ; x ) $\Phi _{n,q}((t-x)^{m};x)$ for m = 1 , 2 $m=1,2$ . We give estimation for the first and second-order central moments. We present a Korovkin type approximation theorem and give a local approximation theorem by using modulus of continuity. We obtain a local direct estimate for the new Szász–Mirakjan operators in terms of Lipschitz-type maximal function of order α. Finally, we prove a Korovkin type weighted approximation theorem.
Databáze: Directory of Open Access Journals
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