A new type of Szasz-Mirakjan operators based on q-integers

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Sabancigil P., Mahmudov N., Dagbasi G.

JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2023, no.1, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2023 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1186/s13660-023-03053-6
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

In this article, by using the notion of quantum calculus, we define a new type Szasz-Mirakjan operators based on the q-integers. We derive a recurrence formula and calculate the moments Phi(n,q)(t(m); X) for m=0,1,2 and the central moments Phi(n,q)((t-x)(m);X) for 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 Sz & aacute;sz-Mirakjan operators in terms of Lipschitz-type maximal function of order alpha. Finally, we prove a Korovkin type weighted approximation theorem.