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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 5

Characterization of Absolute and Uniform Continuity

Oktay DUMAN
İsmail ASLAN
Sayfa
1550–1565
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

At the end of the paper, we discuss some special cases and applications.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In the present paper, by considering nonlinear integral operators and using their approximations via regular summability methods, we obtain characterizations for some function spaces including the space of absolutely continuous functions, the space of uniformly continuous functions, and their other variants.
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Temel Bulgular & Veri:We observe that Bell-type summability methods are quite effective to generalize and improve some related results in the literature.
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Sonuç & Katkı:At the end of the paper, we discuss some special cases and applications.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Summability process · absolute continuity · uniform continuity

Abstract

In the present paper, by considering nonlinear integral operators and using their approximations via regular summability methods, we obtain characterizations for some function spaces including the space of absolutely continuous functions, the space of uniformly continuous functions, and their other variants. We observe that Bell-type summability methods are quite effective to generalize and improve some related results in the literature. At the end of the paper, we discuss some special cases and applications.

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Bu Makaleye Atıf Yap

DUMAN, O., ASLAN, İ. (2022). Characterization of Absolute and Uniform Continuity. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 5, 1550–1565. https://ajindex.com/articles/529683

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Kaynakça (16)

  1. G.A. Anastassiou and O. Duman, Towards Intelligent Modeling: Statistical Approximation Theory, Intelligent Systems Reference Library, vol. 14, Springer-Verlag, Berlin, 2011
  2. L. Angeloni and G. Vinti, Convergence in variation and rate of approximation for nonlinear integral operators of convolution type, Results Math. 48, 1-23, 2006
  3. L. Angeloni and G. Vinti, Erratum to: Convergence in variation and rate of approximation for nonlinear integral operators of convolution type, Results Math. 57, 387-391, 2010
  4. L. Angeloni and G. Vinti, Variation and approximation in multidimensional setting for Mellin integral operators, New Perspectives on Approximation and Sampling Theory, 299-317, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Cham, 2014
  5. L. Angeloni and G. Vinti, A characterization of absolute continuity by means of Mellin integral operators, Z. Anal. Anwend 34 (3), 343-356, 2015
  6. L. Angeloni and G. Vinti, Convergence in variation and a characterization of the absolute continuity, Integral Transforms Spec. Funct. 26, 829-844, 2015
  7. L. Angeloni and G. Vinti, A concept of absolute continuity and its characterization in terms of convergence in variation, Math. Nachr. 289 (16), 1986-1994, 2016
  8. I. Aslan and O. Duman, A summability process on Baskakov-type approximation, Period. Math. Hungar. 72 (2), 186-199, 2016
  9. I. Aslan and O. Duman, Summability on Mellin-type nonlinear integral operators, Integral Transforms Spec. Funct. 30 (6), 492-511, 2019
  10. I. Aslan and O. Duman, Approximation by nonlinear integral operators via summability process, Math. Nachr., 2020 (in press) doi: 10.1002/mana.201800187
  11. I. Aslan and O. Duman, Nonlinear approximation in N-dimension with the help of summability methods, submitted for publication
  12. Ö.G. Atlihan and C. Orhan, Summation process of positive linear operators, Comput. Math. Appl. 56, 1188-1195, 2008
  13. C. Bardaro, P.L. Butzer and I. Mantellini, The exponential sampling theorem of signal analysis and the reproducing kernel formula in the Mellin transform setting, Sampl Theory Signal Image Process. 13 (1), 35-66, 2014
  14. C. Bardaro, P.L. Butzer, R.L. Stens and G. Vinti, Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals, Analysis 23, 299-340, 2003
  15. H.T. Bell, A−summability, Dissertation, Lehigh University, Bethlehem., Pa., 1971
  16. H.T. Bell, Order summability and almost convergence, Proc. Amer. M