ON SOME RESULTS OF WEIGHTED HÖLDER TYPE INEQUALITY ON TIME SCALES

The concept of time scales has attracted the attention of mathematicians for a quarter-century. The time scales have a very important place in mathematical analysis. Many mathematicians have worked on this subject and they have achieved good results. Inequalities and dynamic equations are at the top of these studies. Inequalities and dynamic equations contributed to the solution of many problems in various branches of science. In this article, some results of weighted Hölder type inequality are presented via ⋄_α-integral.

Keywords:

Hölder type inequality, Time scales Integral inequalities,

PDF

___

[1] Hilger, S. Ein Maßkettenkalkül mit Anwendung auf Zentrmsmannigfaltingkeiten, Ph.D. Thesis, Univarsi. Würzburg, 1988.
[2] Agarwal, R.P., Bohner, M., Peterson, A., “Inequalities on time scales: A survey”. Math. Inequal. Appl., 4, 535-555, 2001.
[3] Akin-Bohner, A., Bohner, M., Akin, F., “Pachpatte inequalities on time scales”. Journal of Inequalities in Pure and Applied Mathematics, 6(1), 1-23, 2005.
[4] Li, W.N., “Nonlinear Integral Inequalities in Two Independent Variables on Time Scales”. Adv Differ Equ. doi:10.1155/2011/283926, 2011.
[5] Anastassiou, G.A., “Principles of delta fractional calculus on time scales and inequalities”, Mathematical and Computer Modelling, 52, 556-566, 2010.
[6] Wong, F.-H., Yeh, C.-C.,Yu, S.L.,Hong, C.-H., “Young’s inequality and related results on time scales,” Appl. Math. Lett. 18, 983–988, 2005.
[7] Wong, F.-H., Yeh, C.-C., Lian, W.-C., “An extension of Jensen’s inequality on time scales,” Adv. Dynam. Syst. Appl. 1 (1), 113–120, 2006.
[8] Kuang, J., Applied inequalities, Shandong Science Press, Jinan, 2003.
[9] Uçar, D., Hatipoğlu, V.F., Akincali, A., “Fractional Integral Inequalıties On Tıme Scales.” Open J. Math. Sci.,Vol. 2, No. 1, pp. 361-370, 2018.
[10] Özkan, U.M., Sarikaya, M.Z., Yildirim, H., “Extensions of certain integral inequalities on time scales,” Appl. Math. Lett.,, 21, 993–1000, 2008. . [11] Tian, J.-F., Ha, M.-H., “Extensions of Hölder-type inequalities on time scales and their applications,” J. Nonlinear Sci. Appl.,10, 937–953, 2017.
[12] Kac, V., Cheung, P., Quantum Calculus. Universitext Springer, New York 2002.
[13] Yang, W.-G., “A functional generalization of diamond-α integral Hölder’s inequality on time scales,” Appl. Math. Lett., 23, 1208–1212, 2010.
[14] Bohner, M., Peterson, A., Dynamic equations on time scales, An introduction with applications. Birkhauser, Boston, 2001.
[15] Sheng, Q., Fadag, M., Henderson, J., Davis, J.M., “An exploration of combined dynamic derivatives on time scales and their applications,” Nonlinear Anal. Real World Appl. 7, 395–413, 2006.
[16] Qi, F., “Several integral inequalities.” RGMIA Res. Rep. Coll., 2(7), Art. 9, 1039–1042, 1999. [17] Qi, F., “Several integral inequalities.” J. Inequal. Pure Appl. Math, 1(2), 2000.
[18] Hilger, S., “Analysis on measure chains-a unified approach to continuous and discrete calculus.” Results Math. 18, 18–56, 1990.
[19] Agarwal, R.P., O’Regan, D., Saker, S.H., Dynamic Inequalities on Time Scales, Springer, Heidelberg / New York / Drodrechet/London 2014.
[20] Li, W.N., “Nonlinear Integral Inequalities in Two Independent Variables on Time Scales.” Adv Differ Equ., 283926.. doi:10.1155/2011/283926, 2011. [21] Bohner, M., Agarwal, R.P., “Basic calculus on time scales and some of its applications”. Resultate der Mathematic, 35, 3-22. 1999. [22] Bohner, M., Guseinov, G.S., “Multiple Lebesgue integration on time scales.” Adv. Differ. Equ., 026391, 2006.
[23] Chen, G., Wei, C., “A functional generalization of diamond-α integral Dresher’s inequality on time scales.” Adv. Differ. Equ., 324.doi:10.1186/1687-1847-2014-324, 2014.
[24] Yin, L., Qi, F., “Some Integral Inequalities on Time Scales,” Results. Math., 64,371–381. 2013, DOI 10.1007/s00025-013-0320-z.
[25] Qi, F., Li, A.-J., Zhao, W.-Z., Niu, D.-W., Cao, J., “Extensions of several integral inequalities.” J. Inequal. Pure Appl. Math. 7(3), Art. 107, 2006. [26] Spedding, V., “Taming nature’s numbers,” New Scientist, July 19, 28–31, 2003.
[27] Tisdell, C.C., Zaidi, A., “Basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling.” Nonlinear Anal., 68, 3504–3524, 2008.
[28] Bohner, M., Heim, J., Liu, A., “Qualitative analysis of Solow model on time scales.” J. Concrete Appl. Math., 13, 183–197, 2015.
[29] Brigo, D., Mercurio, F., “Discrete time vs continuous time stock-price dynamics and implications for option pricing.” Finance Stochast., 4, 147–159, 2000.
[30].Seadawy, A.R., Iqbal, M., Lu, D., “Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity,” Journal of Taibah University for Science, 13:1, 1060-1072, DOI: 10.1080/16583655.2019.1680170, 2019.
[31] Tuna, A., Kutukcu, S., “Some integral inequalities on time scales.” Applied Mathematics and Mechanics (English Edition), 29(1), 23-28, 2008.
[32] Krnıc, M., Pecarıc, J., “General Hilbert’s an Hardy’s inequality.” J. Math Ineq and Appl,, 8:29–51, 2005.

ISSN: 2618-6136
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2015
Yayıncı: INESEG Yayıncılık

Arşiv