Some approximation results for the new modification of bernstein-beta operators
AIMS Mathematics, cilt.7, sa.2, ss.1831-1844, 2022 (SCI-Expanded, SSCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 7 Sayı: 2
- Basım Tarihi: 2022
- Doi Numarası: 10.3934/math.2022105
- Dergi Adı: AIMS Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, Directory of Open Access Journals
- Sayfa Sayıları: ss.1831-1844
- Anahtar Kelimeler: Korovkin type approximation theorem, modulus of continuity, functions of Lipschitz class, Peetre's K-functionals
- Ankara Hacı Bayram Veli Üniversitesi Adresli: Evet
Özet
This paper deals with the newly modification of Beta-type Bernstein operators, preserving constant and Korovkin’s other test functions ei = ti, i = 1, 2 in limit case. Then the uniform convergence of the constructed operators is given. The rate of convergence is obtained in terms of modulus of continuity, Peetre-K functionals and Lipschitz class functions. After that, the Voronovskaya-type asymptotic result for these operators is established. At last, the graphical results of the newly defined operators are discussed.