A new Pachpatte type dynamic inequality on time scales
Keywords:
Time scale; Dynamic inequality; Dynamic equation
Abstract
In this paper, using the comparison theorem, we investigate a new Pachpatte type dynamic inequality on time scales, which provides explicit bounds on unknown functions. Our result unifies and extends a continuous inequality and its corresponding discrete analogues.
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References
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[2] M.Bohner, A.Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston, 2001.
[3] M.Bohner, A.Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003.
[4] W.N.Li, Some new dynamicinequalities on time scales, J.Math.Anal.Appl., 319(2006), 802-814.
[5] W.N.Li, W.Sheng, Some nonlinear dynamic inequalities on time scales, Proc.Indian Acad. Sci., 117(2007), 545-554.
[6] W.N.Li, Some Pachpatte type inequalities on time scales, Comput.Math.Appl. 57(2009), 275-282.
[7] Y.Sun,T.Hassan, Some nonlinear dynamic integral inequalities on time scales, Appl. Math. Comput.,220(2013), 221-225.
[8] J.Gu, F.Meng, Some new nonlinear Volterra-Fredholm type dynamic integral inequalities on time scales, Appl. Math. Comput.,245(2014),235-242.
[9] D.B.Pachpatte, Some new dynamic inequality on time scales in three variables,Journal of Taibah University for Science, 11(2017),1135-1140.
[10] B.G.Pachpatte, Inequalities for Differentialand Integral Equations, Academic Press, New York, 1998.
[11] B.G.Pachpatte, Inequalities for Finite DifferenceEquations, Marcel Dekker Inc., New York, 2002.
[2] M.Bohner, A.Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston, 2001.
[3] M.Bohner, A.Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, 2003.
[4] W.N.Li, Some new dynamicinequalities on time scales, J.Math.Anal.Appl., 319(2006), 802-814.
[5] W.N.Li, W.Sheng, Some nonlinear dynamic inequalities on time scales, Proc.Indian Acad. Sci., 117(2007), 545-554.
[6] W.N.Li, Some Pachpatte type inequalities on time scales, Comput.Math.Appl. 57(2009), 275-282.
[7] Y.Sun,T.Hassan, Some nonlinear dynamic integral inequalities on time scales, Appl. Math. Comput.,220(2013), 221-225.
[8] J.Gu, F.Meng, Some new nonlinear Volterra-Fredholm type dynamic integral inequalities on time scales, Appl. Math. Comput.,245(2014),235-242.
[9] D.B.Pachpatte, Some new dynamic inequality on time scales in three variables,Journal of Taibah University for Science, 11(2017),1135-1140.
[10] B.G.Pachpatte, Inequalities for Differentialand Integral Equations, Academic Press, New York, 1998.
[11] B.G.Pachpatte, Inequalities for Finite DifferenceEquations, Marcel Dekker Inc., New York, 2002.
Published
2018-12-11
How to Cite
Sheng, W., & Li, W. N. (2018). A new Pachpatte type dynamic inequality on time scales. Journal of Progressive Research in Mathematics, 14(2), 2361-2365. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1651
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