Weighted Statistical Relative Invariant Mean in Modular Function Spaces with Related approximation Results

Kadak U.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, cilt.39, sa.11, ss.1181-1207, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 11
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1080/01630563.2018.1470096
  • Dergi Adı: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1181-1207
  • Anahtar Kelimeler: Bivariate type of Stancu-Schurer-Kantorovich operators, double weighted sigma-density, Korovkin-type approximation theorem by double sequences of positive linear operators, relative modular weighted statistical sigma-convergence, relative modular weighted sigma-statistical convergence, TAUBERIAN CONDITIONS, DIFFERENCE OPERATOR, DOUBLE SEQUENCES, CONVERGENCE, SUMMABILITY, THEOREMS, FOLLOWS, CORE, (P
  • Gazi Üniversitesi Adresli: Evet

Özet

The idea of statistical relative convergence on modular spaces has been introduced by Orhan and Demirci. The notion of sigma-statistical convergence was introduced by Mursaleen and Edely and further extended based on a fractional order difference operator by Kadak. The concern of this paper is to define two new summability methods for double sequences by combining the concepts of statistical relative convergence and sigma-statistical convergence in modular spaces. Furthermore, we give some inclusion relations involving the newly proposed methods and present an illustrative example to show that our methods are nontrivial generalizations of the existing results in the literature. We also prove a Korovkin-type approximation theorem and estimate the rate of convergence by means of the modulus of continuity. Finally, using the bivariate type of Stancu-Schurer-Kantorovich operators, we display an example such that our approximation results are more powerful than the classical, statistical, and relative modular cases of Korovkin-type approximation theorems.