Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2021 / Cilt: 70 - Sayı: 1

Chebyshev type inequalities with fractional delta and nabla h-sum operators

Pages
357–365
Publication Date
2021-06-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We give examples to illustrate our results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of this study is to establish new discrete inequalities for synchronous functions using fractional order delta and nabla h-sum operators.
📊
Key Findings & Data:The aim of this study is to establish new discrete inequalities for synchronous functions using fractional order delta and nabla h-sum operators.
💡
Conclusion & Impact:We give examples to illustrate our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fractional h-difference · inequalities · Chebyhev's inequality

Abstract

The aim of this study is to establish new discrete inequalities for synchronous functions using fractional order delta and nabla h-sum operators. We give examples to illustrate our results.

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Cite This Article

ASLIYÜCE, S., GÜVENİLİR, A. F. (2021). Chebyshev type inequalities with fractional delta and nabla h-sum operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 70 - Sayı: 1, 357–365. https://ajindex.com/articles/746753

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References (14)

  1. Anastassiou, G. A., Nabla fractional calculus on time scales and inequalities, J. Concr. Appl. Math., 11(1) (2013), 96-111.
  2. Andric, M., Pecaric, J., Peric, I., A multiple Opial type inequality for the Riemann-Liouville fractional derivatives, J. Math. Inequal., 7(1) (2013), 139-150. https://doi.org/10.7153/jmi-07-13
  3. Aslıyüce, S., Güvenilir, A. F., Chebyshev type inequality on nabla discrete fractional calculus, Fract. Differ. Calc., 6(2) (2016), 275-280. https://doi.org/10.7153/fdc-06-18
  4. Aslıyüce, S., Güvenilir, A. F., Fractional Jensen's Inequality, Palest. J. Math., 7(2) (2018), 554-558.
  5. Aslıyüce, S., Wirtinger type inequalities via fractional integral operators, Stud. Univ. Babes- Bolyai Math., 64(1) (2019) 1, 35-42. https://doi.org/10.24193/subbmath.2019.1.04
  6. Atici, F, M., Eloe, P. W., A transform method in discrete fractional calculus, Int. J. Difference Equ., 2(2007), 165-176.
  7. Atici, F, M., Eloe, P. W., Discrete fractional calculus with the nabla operator, Electron J. Qual. Theory Differ. Equ., 3(2009), 12pp. Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J. J., Fractional Calculus. Models and Numerical Methods. World Scientific Publishing Co. Pte. Ltd., Hackensack, 2017.
  8. Bastos, N. R. O., Ferreira, R. A. C, Torres, D. F. M., Discrete-time fractional variational problems, Signal Processing, 91(2011), 513-524. https://doi.org/10.1016/j.sigpro.2010.05.001
  9. Belarbi, S., Dahmani, Z., On some new fractional integral inequalities, JIPAM. J. Inequal. Pure Appl. Math., 10(3) (2009), Article 86, 5 pp. Bohner, M., Ferreira, R. A. C., Some discrete fractional inequalities of Chebyshev type, Afr. Diaspora J. Math., 11(2) (2011), 132-137.
  10. Chebyshev, P.L., Sur les expressions approximatives des integrales definies par les autres prises entre les memes limites, Proc. Math. Soc. Charkov, 2,(1882), 93-98.
  11. Dragomir, S. S., Crstici, B., A mapping associated to Chebyshev's inequality for integrals, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 10(1999), 63-67.
  12. Dragomir, S. S., Operator Inequalities of the Jensen, Cebyshev and Grüss Type, Springer Briefs in Mathematics. Springer, New York, 2012.
  13. Ferreira, R. A. C., A discrete fractional Gronwall inequality, Proc. Amer. Math. Soc., 140(5) (2012), 1605-1612. https://doi.org/10.1090/S0002-9939-2012-11533-3
  14. Ferreira, R. A. C., Torres, D. F. M., Fractional h-difference equations arising from the calculus of variations, Appl. Anal. Discrete Math., 5(1) (2011), 110-121. https://doi.org/10,2298/AADM110131002F Flores-Franuli