Approximation of Multiple Stancu-Type Bernstein Operators

Özarslan M. A., ÇEKİM B., ÇİT S.

Journal of Function Spaces, cilt.2026, sa.1, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2026 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1155/jofs/2332230
  • Dergi Adı: Journal of Function Spaces
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Middle East & Africa Database (ProQuest), Natural Science Collection (ProQuest), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
  • Anahtar Kelimeler: Beta function, hypergeometric functions, modulus of continuity, multiple Stancu-type Bernstein operators, Peetre′s κ-functional, Sheffer polynomials
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we introduce a new class of multiple Stancu-type Bernstein operators defined via Beta function based integral modification. We study their approximation properties and establish uniform convergence by means of Korovkin′s theorem under suitable conditions on the parameter αη. Rates of convergence are obtained in terms of the modulus of continuity and Peetre′s κ-functional, and a Voronovskaja-type asymptotic formula is derived. Furthermore, we obtain representations of the operator in terms of special functions, which, combined with its moment properties, lead to finite summation formulas for the generalized hypergeometric function 3F2 and coefficient identities associated with the confluent hypergeometric function 1F1. Moreover, the operators unify several classical constructions: They reduce to the multiple Bernstein operators as α⟶0+, and yield a multiple Szász-type operator under an appropriate scaling, recovering a result of (Varma, 2013). Numerical examples and graphical simulations are provided to illustrate the approximation behavior, confirm the theoretical findings, and highlight the crucial role of the parameter αη in controlling the approximation behavior.