Some generalizations of dynamic Opial-type inequalities on time scales
Authors
Y. A. A. Elsaid
- Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Nasr City (11884), Cairo, Egypt.
- Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt.
A. A. S. Zaghrout
- Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Nasr City (11884), Cairo, Egypt.
- Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt.
A. A. El-Deeb
- Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Nasr City (11884), Cairo, Egypt.
- Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt.
Abstract
In this paper, we prove some dynamic Opial type inequalities on time scales. The functions involved in these Opial type inequalities are positive and monotone. In addition to these generalizations, some integral and discrete inequalities will be obtained as special cases of our results.
Share and Cite
ISRP Style
Y. A. A. Elsaid, A. A. S. Zaghrout, A. A. El-Deeb, Some generalizations of dynamic Opial-type inequalities on time scales, Journal of Mathematics and Computer Science, 36 (2025), no. 1, 17--34
AMA Style
Elsaid Y. A. A., Zaghrout A. A. S., El-Deeb A. A., Some generalizations of dynamic Opial-type inequalities on time scales. J Math Comput SCI-JM. (2025); 36(1):17--34
Chicago/Turabian Style
Elsaid, Y. A. A., Zaghrout, A. A. S., El-Deeb, A. A.. "Some generalizations of dynamic Opial-type inequalities on time scales." Journal of Mathematics and Computer Science, 36, no. 1 (2025): 17--34
Keywords
- Opial type inequalities
- dynamic inequalities
- time scale
MSC
References
-
[1]
R. P. Agarwal, V. Lakshmikantham, Uniqueness and nonuniqueness criteria for ordinary differential equations, World Scientific Publishing Co., River Edge, NJ (1993)
-
[2]
R. Agarwal, D. O’Regan, S. Saker, Dynamic inequalities on time scales, Springer, Cham (2014)
-
[3]
R. P. Agarwal, P. Y. H. Pang, Opial inequalities with applications in differential and difference equations, Kluwer Academic Publishers, Dordrecht (1995)
-
[4]
M. H. Ali, H. M. El-Owaidy, H. M. Ahmed, A. A. El-Deeb, I. Samir, Optical solitons and complexitons for generalized Schr¨odinger–Hirota model by the modified extended direct algebraic method, Opt. Quantum Electron., 55 (2023),
-
[5]
P. R. Beesack, On an integral inequality of Z. Opial, Trans. Amer. Math. Soc., 104 (1962), 470–475
-
[6]
M. Bohner, T. S. Hassan, T. Li, Fite-Hille-Wintner-type oscillation criteria for second-order half-linear dynamic equations with deviating arguments, Indag. Math. (N.S.), 29 (2018), 548–560
-
[7]
M. Bohner, B. Kaymakc¸alan, Opial inequalities on time scales, Ann. Polon. Math., 77 (2001), 11–20
-
[8]
M. Bohner, T. Li, Kamenev-type criteria for nonlinear damped dynamic equations, Sci. China Math., 58 (2015), 1445–1452
-
[9]
M. Bohner, A. Peterson, Advances in dynamic equations on time scales, Birkh¨auser Boston, Boston, MA (2003)
-
[10]
M. Bohner, A. Peterson, Dynamic equations on time scales: An introduction with applications, Birkh¨auser, Boston (2001)
-
[11]
M. Bohner, A. Peterson, Dynamic equations on time scales, Birkh¨auser Boston, Boston, MA (2001)
-
[12]
A. A El-Deeb, H. A. Elsennary, D. Baleanu, Some new Hardy-type inequalities on time scales, Adv. Difference Equ., 2020 (2020), 21 pages
-
[13]
A. A. El-Deeb, H. A. El-Sennary, Z. A. Khan, Some Steffensen-type dynamic inequalities on time scales, Adv. Difference Equ., 2019 (2019), 14 pages
-
[14]
A. A. El-Deeb, H. A. El-Sennary, Z. A. Khan, Some reverse inequalities of Hardy type on time scales, Adv. Difference Equ., 2020 (2020), 18 pages
-
[15]
L.-G. Hua, On an inequality of Opial, Sci. Sinica, 14 (1965), 789–790
-
[16]
V. Kac, P. Cheung, Quantum calculus, Springer-Verlag, New York (2002)
-
[17]
A. Lasota, A discrete boundary value problem, Ann. Polon. Math., 20 (1968), 183–190
-
[18]
N. Levinson, On an inequality of Opial and Beesack, Proc. Amer. Math. Soc., 15 (1964), 565–566
-
[19]
J. D. Li, Opial-type integral inequalities involving several higher order derivatives, J. Math. Anal. Appl., 67 (1992), 98–110
-
[20]
C. L. Mallows, An even simpler proof of Opial’s inequality, Proc. Amer. Math. Soc., 16 (1965), 173
-
[21]
P. Maroni, Sur l’in´egalit´e d’Opial-Beesack, C. R. Acad. Sci. Paris S´er. A-B, 264 (1967), A62–A64
-
[22]
Z. Olech, A simple proof of a certain result of Z. Opial, Ann. Polon. Math., 8 (1960), 61–63
-
[23]
Z. Opial, Sur une in´egalit´, Ann. Polon. Math., 8 (1960), 29–32
-
[24]
R. N. Pederson, On an inequality of Opial, Beesack and Levinson, Proc. Amer. Math. Soc., 16 (1965), 174
-
[25]
G.-S. Yang, On a certain result of Z. Opial, Proc. Japan Acad., 42 (1966), 78–83
-
[26]
D. Zhao, T. An, G. Ye, W. Liu, Some generalizations of Opial type inequalities for interval-valued functions, Fuzzy Sets and Systems, 436 (2022), 128–151