GENERALIZED ALMOST CONVERGENCE OF DOUBLE SEQUENCES IN MODULAR FUNCTION SPACES

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Kadak U.

ADVANCES IN OPERATOR THEORY, cilt.4, sa.3, ss.556-573, 2019 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 4 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.15352/aot.1808-1412
  • Dergi Adı: ADVANCES IN OPERATOR THEORY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.556-573
  • Anahtar Kelimeler: Korovkin-type approximation theorem, almost convergence, fractional-order difference operator, modular function space, bivariate Chlodowsky-Szsaz-Kantorovich-Charlier-type operator
  • Gazi Üniversitesi Adresli: Evet

Özet

This article deals with almost convergence of double sequences using a new generalization of fractional-order difference operator in modular spaces and application to the Korovkin-type approximation in the context of modular spaces for positive linear operators. We then obtain several inclusion relations and present some examples, include proper non-trivial extensions of the corresponding classical ones. Further, we extend our study to new modular forms of Korovkin-type approximation theorems. Finally, we give an example using bivariate Chlodowsky-Szsaz-Kantorovich-Charlier-type operators and outline possible further extensions and improvements, in order to illustrate the effectiveness of the proposed methods.