Statistical Convergence with Respect to Power Series Methods and Applications to Approximation Theory

ÜNVER M., ORHAN C.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, cilt.40, sa.5, ss.535-547, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 5
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1080/01630563.2018.1561467
  • Dergi Adı: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.535-547
  • Anahtar Kelimeler: Korovkin type approximation, power series method, statistical convergence, strong convergence, uniform integrability, ABEL TRANSFORMS, SUMMABILITY, OPERATORS
  • Ankara Üniversitesi Adresli: Evet

Özet

In this article we introduce the concepts of -statistical convergence and P-p-strong convergence that are introduced via power series methods. Introducing a new type of uniform integrability with the help of power series method we obtain a relationship between these concepts which is actually a characterization of the concept of P-p-strong convergence. As an application we give a Korovkin type approximation theorem by using P-p-statistical convergence and also present an example to illustrate that P-p-statistical approximation is stronger than uniform approximation.