Approximation properties of a generalization of positive linear operators

Dogru O.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.342, sa.1, ss.161-170, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 342 Sayı: 1
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1016/j.jmaa.2007.12.007
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.161-170
  • Anahtar Kelimeler: sequence of positive linear operators, Korovkin theorem, weighted Korovkin type theorem, modulus of continuity, Lipschitz type maximal functions, Voronovskaja type asymptotic formulas, ZELLER OPERATORS, MEYER-KONIG, GENERATING-FUNCTIONS
  • Gazi Üniversitesi Adresli: Evet

Özet

In the present paper we introduce a generalization of positive linear operators and obtain its Korovkin type approximation properties. The rates of convergence of this generalization is also obtained by means of modulus of continuity and Lipschitz type maximal functions. The second purpose of this paper is to obtain weighted approximation properties for the generalization of positive linear operators defined in this paper. Also we obtain a differential equation so that the second moment of our operators is a particular solution of it. Lastly, some Voronovskaja type asymptotic formulas are obtained for Meyer-Konig and Zeller type and Bleimann, Butzer and Hahn type operators. (C) 2007 Elsevier Inc. All rights reserved.