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.
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
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.
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.
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
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.