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Year 2020, Volume: 3 Issue: 1, 141 - 144, 15.12.2020

Lütfi Akın

Abstract

References

  • 1 S.Hilger, Ein Maßkettenkalkul mit Anwendung auf Zentrmsmannigfaltingkeiten, Ph.D. Thesis, Univarsi. Wurzburg, 1988.
  • 2 R.P. Agarwal, M. Bohner, A. Peterson, Inequalities on time scales: A survey. Math. Inequal. Appl., 4, (2001), 535-555. https://doi.org/10.7153/mia-04-48.
  • 3 E. Akin-Bohner, M. Bohner, F. Akin, Pachpatte inequalities on time scales. Journal of Inequalities in Pure and Applied Mathematics. 6(1),(2005),1-23.
  • 4 W.N.Li,Nonlinear Integral Inequalities in Two Independent Variables on Time Scales. Adv Differ Equ.283926, (2011). doi:10.1155/2011/283926.
  • 5 G.A. Anastassiou, Principles of delta fractional calculus on time scales and inequalities.Mathematical and Computer Modelling. 52, (2010), 556-566. https://doi.org/10.1016/j.mcm.2010.03.055.
  • 6 F.-H. Wong, C.-C. Yeh, S.-L.Yu, C.-H. Hong, Young’s inequality and related results on time scales, Appl. Math. Lett. 18, (2005), 983-988.
  • 7 F.-H. Wong, C.-C. Yeh, W.-C. Lian, An extension of Jensen’s inequality on time scales, Adv. Dynam. Syst. Appl. 1(1), (2006), 113-120.
  • 8 J. Kuang, Applied inequalities, Shandong Science Press, Jinan, 2003.
  • 9 D. Ucar, V.F. Hatipoglu, A. Akincali, Fractional Integral Inequalıties On Tıme Scales. Open J. Math. Sci., 2(1), (2018), 361-370.
  • 10 U.M. Ozkan, M.Z. Sarikaya, H. Yildirim, Extensions of certain integral inequalities on time scales, Appl. Math. Lett., 21, (2008), 993-1000.
  • 11 J.-F. Tian, M.-H. Ha, Extensions of Holder-type inequalities on time scales and their applications, J. Nonlinear Sci. Appl., 10, (2017), 937-953.
  • 12 V. Kac, P. Cheung, Quantum Calculus. Universitext Springer, New York 2002.
  • 13 W.-G. Yang, A functional generalization of diamond-integral Holdera’s inequality on time scales, Appl. Math. Lett., 23, (2010),1208-1212.
  • 14 A. Tuna, S. Kutukcu, Some integral inequalities on time scales, Applied Mathematics and Mechanics (English Edition), 29(1), (2008),23-28.
  • 15 G.-Sheng Chen,Some improvements of Minkowski’s integral inequality on time scales, Journal of Inequalities and Applications, 2013:318,(2013),1-6. http://www.journalofinequalitiesandapplications.com/content/2013/1/318.
  • 16 M. Bohner, R.P. Agarwal, Basic calculus on time scales and some of its applications,Resultate der Mathematic, 35, (1999),3-22. Doi.org/10.1007/BF03322019.
  • 17 M. Bohner, A. Peterson, Dynamic equations on time scales, An introduction with applications. Birkhauser, Boston, 2001. https://doi.org/10.1007/978-1-4612-0201-1.
  • 18 L. Akin,On the Fractional Maximal Delta Integral Type Inequalities on Time Scales, Fractal and fractional, 4(2), (2020),1-10.
  • 19 L. Akin,On Some Results of Weighted Holder Type Inequality on Time Scales, Middle East Journal of Science,6(1), (2020),15-22.

On Some Integral Type Inequality on Time Scales

Year 2020, Volume: 3 Issue: 1, 141 - 144, 15.12.2020

Lütfi Akın

Abstract

Time scales have been in the study area of many mathematicians for the last 30 years. Some of these studies are inequalities and dynamic equations. And also, inequalities and dynamic equations, differential calculus, difference calculus and quantum calculus contributed to the solution of many problems in various branches of science. Dynamic equations and inequalities on time scales have many applications in quantum mechanics, neural networks, heat transfer, electrical engineering, optics, economics and population dynamics. It is possible to give an example from the economics, seasonal investments and incomes. In this study, we will prove a special case of inequalities Minkowski’s integral type on time scale via the delta integral.

Keywords

Integral type inequality Time scales Integral inequalities.

References

  • 1 S.Hilger, Ein Maßkettenkalkul mit Anwendung auf Zentrmsmannigfaltingkeiten, Ph.D. Thesis, Univarsi. Wurzburg, 1988.
  • 2 R.P. Agarwal, M. Bohner, A. Peterson, Inequalities on time scales: A survey. Math. Inequal. Appl., 4, (2001), 535-555. https://doi.org/10.7153/mia-04-48.
  • 3 E. Akin-Bohner, M. Bohner, F. Akin, Pachpatte inequalities on time scales. Journal of Inequalities in Pure and Applied Mathematics. 6(1),(2005),1-23.
  • 4 W.N.Li,Nonlinear Integral Inequalities in Two Independent Variables on Time Scales. Adv Differ Equ.283926, (2011). doi:10.1155/2011/283926.
  • 5 G.A. Anastassiou, Principles of delta fractional calculus on time scales and inequalities.Mathematical and Computer Modelling. 52, (2010), 556-566. https://doi.org/10.1016/j.mcm.2010.03.055.
  • 6 F.-H. Wong, C.-C. Yeh, S.-L.Yu, C.-H. Hong, Young’s inequality and related results on time scales, Appl. Math. Lett. 18, (2005), 983-988.
  • 7 F.-H. Wong, C.-C. Yeh, W.-C. Lian, An extension of Jensen’s inequality on time scales, Adv. Dynam. Syst. Appl. 1(1), (2006), 113-120.
  • 8 J. Kuang, Applied inequalities, Shandong Science Press, Jinan, 2003.
  • 9 D. Ucar, V.F. Hatipoglu, A. Akincali, Fractional Integral Inequalıties On Tıme Scales. Open J. Math. Sci., 2(1), (2018), 361-370.
  • 10 U.M. Ozkan, M.Z. Sarikaya, H. Yildirim, Extensions of certain integral inequalities on time scales, Appl. Math. Lett., 21, (2008), 993-1000.
  • 11 J.-F. Tian, M.-H. Ha, Extensions of Holder-type inequalities on time scales and their applications, J. Nonlinear Sci. Appl., 10, (2017), 937-953.
  • 12 V. Kac, P. Cheung, Quantum Calculus. Universitext Springer, New York 2002.
  • 13 W.-G. Yang, A functional generalization of diamond-integral Holdera’s inequality on time scales, Appl. Math. Lett., 23, (2010),1208-1212.
  • 14 A. Tuna, S. Kutukcu, Some integral inequalities on time scales, Applied Mathematics and Mechanics (English Edition), 29(1), (2008),23-28.
  • 15 G.-Sheng Chen,Some improvements of Minkowski’s integral inequality on time scales, Journal of Inequalities and Applications, 2013:318,(2013),1-6. http://www.journalofinequalitiesandapplications.com/content/2013/1/318.
  • 16 M. Bohner, R.P. Agarwal, Basic calculus on time scales and some of its applications,Resultate der Mathematic, 35, (1999),3-22. Doi.org/10.1007/BF03322019.
  • 17 M. Bohner, A. Peterson, Dynamic equations on time scales, An introduction with applications. Birkhauser, Boston, 2001. https://doi.org/10.1007/978-1-4612-0201-1.
  • 18 L. Akin,On the Fractional Maximal Delta Integral Type Inequalities on Time Scales, Fractal and fractional, 4(2), (2020),1-10.
  • 19 L. Akin,On Some Results of Weighted Holder Type Inequality on Time Scales, Middle East Journal of Science,6(1), (2020),15-22.
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Lütfi Akın

Publication Date December 15, 2020
Acceptance Date September 26, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Akın, L. (2020). On Some Integral Type Inequality on Time Scales. Conference Proceedings of Science and Technology, 3(1), 141-144.
AMA Akın L. On Some Integral Type Inequality on Time Scales. Conference Proceedings of Science and Technology. December 2020;3(1):141-144.
Chicago Akın, Lütfi. “On Some Integral Type Inequality on Time Scales”. Conference Proceedings of Science and Technology 3, no. 1 (December 2020): 141-44.
EndNote Akın L (December 1, 2020) On Some Integral Type Inequality on Time Scales. Conference Proceedings of Science and Technology 3 1 141–144.
IEEE L. Akın, “On Some Integral Type Inequality on Time Scales”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 141–144, 2020.
ISNAD Akın, Lütfi. “On Some Integral Type Inequality on Time Scales”. Conference Proceedings of Science and Technology 3/1 (December 2020), 141-144.
JAMA Akın L. On Some Integral Type Inequality on Time Scales. Conference Proceedings of Science and Technology. 2020;3:141–144.
MLA Akın, Lütfi. “On Some Integral Type Inequality on Time Scales”. Conference Proceedings of Science and Technology, vol. 3, no. 1, 2020, pp. 141-4.
Vancouver Akın L. On Some Integral Type Inequality on Time Scales. Conference Proceedings of Science and Technology. 2020;3(1):141-4.
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