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Approximation via statistical measurable convergence with respect to power series for double sequences

  • Devia Narrania ORCID logo und Kuldip Raj ORCID logo EMAIL logo
Veröffentlicht/Copyright: 29. März 2023
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 36 Heft 1

Abstract

In this paper, we introduce and study a new type of convergences using statistical convergence via the power series method and measurable convergence. We also study their relationship with other convergences. Further, we demonstrate Korovkin-type approximation theorems for double sequences of positive linear operators using these newly specified convergences, and we also provide illustrations that demonstrate how our proven theorems are better than their classical counterparts. Finally, we have determined rates of statistical product measurable convergence using the power series approach and the modulus of continuity.

Keywords: Double sequences of functions; statistical measurable convergence; Korovkin-type theorem; power series method; rate of convergence
MSC 2010: 40G10; 41A36

Communicated by Siegfried Echterhoff

Funding statement: The first author thanks the Council of Scientific and Industrial Research (CSIR), India for partial support under Grant No. 09/1046(13736)/2022-EMR-I, dated 08/04/2022.

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Received: 2022-12-06
Published Online: 2023-03-29
Published in Print: 2024-01-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. On Mukhin’s necessary and sufficient condition for the validity of the local limit theorem
  3. Non-commutative Khinchine-type inequality for dependent random variables and overview of its applications in data science
  4. Connections and genuinely ramified maps of curves
  5. Caustics of pseudo-spherical surfaces in the Euclidean 3-space
  6. On liftings of modular forms and Weil representations
  7. Approximation via statistical measurable convergence with respect to power series for double sequences
  8. Global existence, scattering, rigidity and inverse scattering for some quasilinear hyperbolic systems
  9. Gem-induced trisections of compact PL 4-manifolds
  10. Categories of modules, comodules and contramodules over representations
  11. On the Iwasawa invariants of BDP Selmer groups and BDP p-adic L-functions
  12. On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms
  13. Congruence subgroups and crystallographic quotients of small Coxeter groups
  14. Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ2
  15. Hardy and BMO spaces on Weyl chambers
  16. De Branges–Rovnyak spaces and local Dirichlet spaces of higher order
https://doi.org/10.1515/forum-2022-0368
Schlagwörter für diesen Artikel
Double sequences of functions; statistical measurable convergence; Korovkin-type theorem; power series method; rate of convergence

Artikel in diesem Heft

  1. Frontmatter
  2. On Mukhin’s necessary and sufficient condition for the validity of the local limit theorem
  3. Non-commutative Khinchine-type inequality for dependent random variables and overview of its applications in data science
  4. Connections and genuinely ramified maps of curves
  5. Caustics of pseudo-spherical surfaces in the Euclidean 3-space
  6. On liftings of modular forms and Weil representations
  7. Approximation via statistical measurable convergence with respect to power series for double sequences
  8. Global existence, scattering, rigidity and inverse scattering for some quasilinear hyperbolic systems
  9. Gem-induced trisections of compact PL 4-manifolds
  10. Categories of modules, comodules and contramodules over representations
  11. On the Iwasawa invariants of BDP Selmer groups and BDP p-adic L-functions
  12. On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms
  13. Congruence subgroups and crystallographic quotients of small Coxeter groups
  14. Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ2
  15. Hardy and BMO spaces on Weyl chambers
  16. De Branges–Rovnyak spaces and local Dirichlet spaces of higher order
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