Riemann-Liouville Type Fractional Generalized λ-Bernstein-Kantorovich Operators

Özger F., Aslan R.

8th International conference Approximation Theory and Special Functions, ATSF 2024, Ankara, Türkiye, 4 - 07 Eylül 2024, cilt.503 PROMS, ss.183-204, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 503 PROMS
  • Doi Numarası: 10.1007/978-3-031-93279-3_9
  • Basıldığı Şehir: Ankara
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.183-204
  • Anahtar Kelimeler: Fractional approximation theory, Operator convergence, Riemann-Liouville operators, Shape parameter in approximation
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Approximation theory, with roots in the Weierstrass theorem, has evolved to encompass various types of polynomial operators, among which the Bernstein polynomials have become particularly influential due to their stability and convergence characteristics. With the addition of shape parameters such as λ and fractional parameters inspired by fractional calculus, modern approximation theory now accommodates complex function behaviors that traditional integer-order operators could not capture. This chapter focuses on the development of new Riemann-Liouville-type fractional λ-Bernstein-Kantorovich operators. It provides detailed proofs of their convergence, pointwise estimates, and asymptotic behavior. Using thorough mathematical analysis, we present direct approximation results, highlighting how these operators effectively approximate functions in different function spaces.