Approximation of Continuous Periodic Functions of Two Variables via Power Series Methods of Summability

Yavuz E., Talo Ö.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.42, no.4, pp.1709-1717, 2019 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1007/s40840-017-0577-6
  • Journal Name: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1709-1717
  • Keywords: Positive linear operators, Korovkin theorem, Power series methods, Double Fourier series
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

We prove a Korovkin-type approximation theorem via power series methods of summability for continuous 2 π-periodic functions of two variables and verify the convergence of approximating double sequences of positive linear operators by using modulus of continuity. An example concerning double Fourier series is also constructed to illustrate the obtained results.