Research Article
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Year 2021, Volume: 70 Issue: 1, 357 - 365, 30.06.2021
https://doi.org/10.31801/cfsuasmas.455707

Abstract

References

  • Anastassiou, G. A., Nabla fractional calculus on time scales and inequalities, J. Concr. Appl. Math., 11(1) (2013), 96-111.
  • 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
  • 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
  • Aslıyüce, S., Güvenilir, A. F., Fractional Jensen's Inequality, Palest. J. Math., 7(2) (2018), 554-558.
  • 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
  • Atici, F, M., Eloe, P. W., A transform method in discrete fractional calculus, Int. J. Difference Equ., 2(2007), 165-176.
  • 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.
  • 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
  • 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.
  • 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.
  • 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.
  • Dragomir, S. S., Operator Inequalities of the Jensen, Cebyshev and Grüss Type, Springer Briefs in Mathematics. Springer, New York, 2012.
  • 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
  • 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-Franulic, A., Román-Flores, H., A Chebyshev type inequality for fuzzy integrals, Appl. Math. Comput., 190(2) (2007), 1178-1184. https://doi.org/10.1016/j.amc.2007.02.143
  • Gonska, H., Rasa, I., Rusu, M., Chebyshev-Grüss-type inequalities via discrete oscillations, Bul. Acad. ¸Stiin¸te Repub. Mold. Mat., 74(1) (2014), 63-89.
  • Goodrich, C., Peterson, A. C., Discrete Fractional Calculus, Springer, Cham, 2015.
  • Mozyrska, D., Girejko, E., Overview of Fractional h-Difference Operators., Advances in Harmonic Analysis and Operator Theory, 253-268, Oper. Theory Adv. Appl., 229, Birkhäuser/Springer Basel AG, Basel, 2013.
  • Persson, L., Oinarov, R., Shaimardan, S., Hardy-type inequalities in fractional h-discrete calculus, J. Inequal. Appl., 2018(73) (2018), 14 pp. https://doi.org/10.1186/s13660-018-1662- 6
  • Podlubny, I. Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applica- tions, Academic Press, San Diego, CA, 1999.
  • Suwan, I., Owies, S., Abdeljawad, T., Monotonicity results for h-discrete fractional operators and application, Adv Di¤ er Equ., (2018) 2018: 207. https://doi.org/10.1186/s13662-018-1660-5
  • Wen, J. J., Pecaric, J., Han, T. Y., Weak monotonicity and Chebyshev type inequality, Math. Inequal. Appl., 18(1) (2015), 217-231. https://doi.org/10.7153/mia-18-16

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

Year 2021, Volume: 70 Issue: 1, 357 - 365, 30.06.2021
https://doi.org/10.31801/cfsuasmas.455707

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.

References

  • Anastassiou, G. A., Nabla fractional calculus on time scales and inequalities, J. Concr. Appl. Math., 11(1) (2013), 96-111.
  • 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
  • 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
  • Aslıyüce, S., Güvenilir, A. F., Fractional Jensen's Inequality, Palest. J. Math., 7(2) (2018), 554-558.
  • 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
  • Atici, F, M., Eloe, P. W., A transform method in discrete fractional calculus, Int. J. Difference Equ., 2(2007), 165-176.
  • 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.
  • 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
  • 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.
  • 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.
  • 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.
  • Dragomir, S. S., Operator Inequalities of the Jensen, Cebyshev and Grüss Type, Springer Briefs in Mathematics. Springer, New York, 2012.
  • 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
  • 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-Franulic, A., Román-Flores, H., A Chebyshev type inequality for fuzzy integrals, Appl. Math. Comput., 190(2) (2007), 1178-1184. https://doi.org/10.1016/j.amc.2007.02.143
  • Gonska, H., Rasa, I., Rusu, M., Chebyshev-Grüss-type inequalities via discrete oscillations, Bul. Acad. ¸Stiin¸te Repub. Mold. Mat., 74(1) (2014), 63-89.
  • Goodrich, C., Peterson, A. C., Discrete Fractional Calculus, Springer, Cham, 2015.
  • Mozyrska, D., Girejko, E., Overview of Fractional h-Difference Operators., Advances in Harmonic Analysis and Operator Theory, 253-268, Oper. Theory Adv. Appl., 229, Birkhäuser/Springer Basel AG, Basel, 2013.
  • Persson, L., Oinarov, R., Shaimardan, S., Hardy-type inequalities in fractional h-discrete calculus, J. Inequal. Appl., 2018(73) (2018), 14 pp. https://doi.org/10.1186/s13660-018-1662- 6
  • Podlubny, I. Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applica- tions, Academic Press, San Diego, CA, 1999.
  • Suwan, I., Owies, S., Abdeljawad, T., Monotonicity results for h-discrete fractional operators and application, Adv Di¤ er Equ., (2018) 2018: 207. https://doi.org/10.1186/s13662-018-1660-5
  • Wen, J. J., Pecaric, J., Han, T. Y., Weak monotonicity and Chebyshev type inequality, Math. Inequal. Appl., 18(1) (2015), 217-231. https://doi.org/10.7153/mia-18-16
There are 24 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Serkan Aslıyüce 0000-0003-1729-3914

Ayşe Feza Güvenilir This is me 0000-0003-2670-5570

Publication Date June 30, 2021
Submission Date August 29, 2018
Acceptance Date February 17, 2021
Published in Issue Year 2021 Volume: 70 Issue: 1

Cite

APA Aslıyüce, S., & Güvenilir, 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, 70(1), 357-365. https://doi.org/10.31801/cfsuasmas.455707
AMA Aslıyüce S, Güvenilir AF. Chebyshev type inequalities with fractional delta and nabla h-sum operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2021;70(1):357-365. doi:10.31801/cfsuasmas.455707
Chicago Aslıyüce, Serkan, and Ayşe Feza Güvenilir. “Chebyshev Type Inequalities With Fractional Delta and Nabla H-Sum Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 1 (June 2021): 357-65. https://doi.org/10.31801/cfsuasmas.455707.
EndNote Aslıyüce S, Güvenilir AF (June 1, 2021) Chebyshev type inequalities with fractional delta and nabla h-sum operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 357–365.
IEEE S. Aslıyüce and A. F. Güvenilir, “Chebyshev type inequalities with fractional delta and nabla h-sum operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 1, pp. 357–365, 2021, doi: 10.31801/cfsuasmas.455707.
ISNAD Aslıyüce, Serkan - Güvenilir, Ayşe Feza. “Chebyshev Type Inequalities With Fractional Delta and Nabla H-Sum Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (June 2021), 357-365. https://doi.org/10.31801/cfsuasmas.455707.
JAMA Aslıyüce S, Güvenilir AF. Chebyshev type inequalities with fractional delta and nabla h-sum operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:357–365.
MLA Aslıyüce, Serkan and Ayşe Feza Güvenilir. “Chebyshev Type Inequalities With Fractional Delta and Nabla H-Sum Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 1, 2021, pp. 357-65, doi:10.31801/cfsuasmas.455707.
Vancouver Aslıyüce S, Güvenilir AF. Chebyshev type inequalities with fractional delta and nabla h-sum operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):357-65.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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