DEGREE OF APPROXIMATION FOR BIVARIATE SZASZ-KANTOROVICH TYPE BASED ON BRENKE TYPE POLYNOMIALS


Begen S., İnce İlarslan H. G.

HONAM MATHEMATICAL JOURNAL, vol.42, pp.251-268, 2020 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 42
  • Publication Date: 2020
  • Doi Number: 10.5831/hmj.2020.42.2.251
  • Journal Name: HONAM MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.251-268
  • Keywords: Szasz-Kantorovich operators, Brenke polynomials, complete modulus of continuity, partial modulus of continuity, Peetre's K-functional, GBS operators, B-continuity, mixed modulus of continuity, Lipschitz class of B-continuous functions, OPERATORS, VARIANT
  • Gazi University Affiliated: Yes

Abstract

In this paper, we estimate the degree of approximation by means of the complete modulus of continuity, the partial modulus of continuity, the Lipschitz-type class and Petree's K-functional for the bivariate Szasz-Kantorovich operators based on Brenke-type polynomials. Later, we construct Generalized Boolean Sum operators associated with combinations of the Szasz-Kantorovich operators based on Brenke-type polynomials. In addition, we obtain the rate of convergence for the GBS operators with the help of the mixed modulus of continuity and the Lipschitz class of the Bogel continuous functions.