Korovkin Type Theorems for Cheney-Sharma Operators via Summability Methods

Soylemez D., ÜNVER M.

RESULTS IN MATHEMATICS, cilt.72, sa.3, ss.1601-1612, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 72 Sayı: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s00025-017-0733-1
  • Dergi Adı: RESULTS IN MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1601-1612
  • Anahtar Kelimeler: Cheney-Sharma operators, Korovkin type theorem, statistical convergence, Abel convergence, POSITIVE LINEAR-OPERATORS, STATISTICAL CONVERGENCE, ABEL TRANSFORMS, APPROXIMATION
  • Ankara Üniversitesi Adresli: Evet

Özet

Korovkin type approximation theory is concerned with the convergence of the sequences of positive linear operators to the identity operator. In this paper, we deal with the Korovkin type approximation properties of the Cheney-Sharma operators by using A-statistical convergence and Abel convergence that are some well known methods of summability theory. We also study the rate of convergence. Finally, we show that the results obtained in this paper are stronger than previous ones and we support our results with particular examples and graphs.