Generalization of Szász–Mirakjan operators and their approximation properties

Mahmudov N., Kara M.

Journal of Analysis, vol.33, no.4, pp.1687-1710, 2025 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 4
  • Publication Date: 2025
  • Doi Number: 10.1007/s41478-025-00890-0
  • Journal Name: Journal of Analysis
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.1687-1710
  • Keywords: Modulus of continuity, Szász–Mirakjan operators, Weighted approximation
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

In this article, we introduce new generalization of Szász–Mirakjan operators. First, we give the recurrence relationship for the moments of these operators and present the central moments up to the fourth degree. Then, we give the local approximation properties of these operators through Peetre’s K-function. Furthermore, we investigate rate of convergence by using modulus of continuity and Lipschitz type maximal functions. Then, we investigate approximation properties of these operators on weighted space. Also, we prove voronoskaja type theorem. Additionally, the bivariate type of these operators is introduced, and the approximate behaviors of these operators are examined. Finally, we give some numerical illustrative examples.