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Journal articles on the topic 'Opial inequalities'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Koliha, J. J., and J. Pecaric. "Weighted Opial inequalities." Tamkang Journal of Mathematics 33, no. 1 (March 31, 2002): 83–92. http://dx.doi.org/10.5556/j.tkjm.33.2002.308.

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This paper presents a class of very general weighted Opial type inequalities. The notivation comes from the monograph of Agarwal and Pang (Opial Inequalities with Applications in Differential and Difference Equations, Kluwer Acad., Dordrecht 1995) and the work of Anastassiou and Pecaric (J. Math. Anal. Appl. 239 (1999), 402-418). Assuming only a very general inequality, we extend the latter paper in several directions. A new result generalizing the original Opial's inequality is obtained, and applications to fractional derivatives are given.

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2

Sayed, A. G., S. H. Saker, and A. M. Ahmed. "Fractional Opial dynamic inequalities." Journal of Mathematics and Computer Science 22, no. 04 (September 5, 2020): 363–80. http://dx.doi.org/10.22436/jmcs.022.04.05.

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3

Anastassiou, George A., Gisèle Ruiz Goldstein, and Jerome A. Goldstein. "Multidimensional weighted Opial inequalities." Applicable Analysis 85, no. 5 (May 2006): 579–91. http://dx.doi.org/10.1080/00036810500345368.

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4

Anastassiou, George A. "Balanced fractional opial inequalities." Chaos, Solitons & Fractals 42, no. 3 (November 2009): 1523–28. http://dx.doi.org/10.1016/j.chaos.2009.03.047.

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5

Alp, Necmettin, Candan Bilişik, and Mehmet Sarıkaya. "On q-Opial type inequality for quantum integral." Filomat 33, no. 13 (2019): 4175–84. http://dx.doi.org/10.2298/fil1913175a.

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6

Zhao, Chang-Jian, Yue-Sheng Wu, and Wing-Sum Cheung. "On Opial-Rozanova type inequalities." Journal of Nonlinear Sciences and Applications 09, no. 05 (May 20, 2016): 2099–104. http://dx.doi.org/10.22436/jnsa.009.05.15.

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7

Zhao, Changjian. "On Opial-Wirtinger type inequalities." AIMS Mathematics 5, no. 2 (2020): 1275–83. http://dx.doi.org/10.3934/math.2020087.

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8

Bohner, Martin, and Bıllûr Kaymakçalan. "Opial inequalities on time scales." Annales Polonici Mathematici 77, no. 1 (2001): 11–20. http://dx.doi.org/10.4064/ap77-1-2.

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9

Cheung, Wing-Sum. "Some new Opial‐type inequalities." Mathematika 37, no. 1 (June 1990): 136–42. http://dx.doi.org/10.1112/s0025579300012869.

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10

Cheung, Wing-Sum, and Chang-Jian Zhao. "On Opial-Type Integral Inequalities." Journal of Inequalities and Applications 2007 (2007): 1–16. http://dx.doi.org/10.1155/2007/38347.

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11

Anastassiou, George A. "Opial Type Inequalities for Semigroups." Semigroup Forum 75, no. 3 (December 2007): 624–33. http://dx.doi.org/10.1007/s00233-007-0727-5.

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12

Brnetić, Ilko, and Josip Pečarić. "Some new Opial-type inequalities." Mathematical Inequalities & Applications, no. 3 (1998): 385–90. http://dx.doi.org/10.7153/mia-01-37.

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13

Cheung, Wing-Sum. "Some generalized Opial-type inequalities." Journal of Mathematical Analysis and Applications 162, no. 2 (December 1991): 317–21. http://dx.doi.org/10.1016/0022-247x(91)90152-p.

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14

Pachpatte, B. G. "On Opial-type integral inequalities." Journal of Mathematical Analysis and Applications 120, no. 2 (December 1986): 547–56. http://dx.doi.org/10.1016/0022-247x(86)90176-9.

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15

Pachpatte, B. G. "On multidimensional Opial-type inequalities." Journal of Mathematical Analysis and Applications 126, no. 1 (August 1987): 85–89. http://dx.doi.org/10.1016/0022-247x(87)90076-x.

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16

Sinnamon, Gord. "Reduction of Opial-type inequalities to norm inequalities." Proceedings of the American Mathematical Society 132, no. 2 (September 5, 2003): 375–79. http://dx.doi.org/10.1090/s0002-9939-03-07184-3.

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17

Saker, S. H., A. G. Sayed, A. Sikorska-Nowak, and I. Abohela. "New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations." Discrete Dynamics in Nature and Society 2019 (August 1, 2019): 1–13. http://dx.doi.org/10.1155/2019/6757080.

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In this paper, we prove that the solvability of dynamic equations of second order is sufficient for the validity of some Hardy and Opial type inequalities with two different weights on time scales. In particular, the results give new characterizations of two different weights in inequalities containing Hardy and Opial operators. The main contribution in this paper is the characterizations of weights in discrete inequalities that will be formulated from our results as special cases.

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18

Pachpatte, B. G. "On Opial type inequalities in two independent variables." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 100, no. 3-4 (1985): 263–70. http://dx.doi.org/10.1017/s0308210500013809.

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SynopsisThe aim of the present paper is to establish some new integral inequalities of Opial type in two independent variables. Our results are the two independent variable generalizations of some of the inequalities recently established by the present author and in special cases yield the two independent variable analogue of the Opial inequality and its generalization given by G. S. Yang.

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19

Bloom, Steven. "First and second order Opial inequalities." Studia Mathematica 126, no. 1 (1997): 27–50. http://dx.doi.org/10.4064/sm-126-1-27-50.

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20

Cheung, Wing-Sum, Zhao Dandan, and Josip Pečarić. "Opial-type inequalities for differential operators." Nonlinear Analysis: Theory, Methods & Applications 66, no. 9 (May 2007): 2028–39. http://dx.doi.org/10.1016/j.na.2006.02.040.

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21

Anastassiou, G. A., J. J. Koliha, and J. Pecaric. "Opial typeLp-inequalities for fractional derivatives." International Journal of Mathematics and Mathematical Sciences 31, no. 2 (2002): 85–95. http://dx.doi.org/10.1155/s016117120201311x.

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This paper presents a class ofLp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of the index law for fractional derivatives in lieu of Taylor's formula, which enables us to relax restrictions on the orders of fractional derivatives.

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22

Atasever, Nuriye, Billur Kaymakcalan, Goran Lesaja, and Kenan Tas. "Generalized diamond-alpha dynamic opial Inequalities." Advances in Difference Equations 2012, no. 1 (2012): 109. http://dx.doi.org/10.1186/1687-1847-2012-109.

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23

Sinnamon, G. J. "Weighted Hardy and Opial-type inequalities." Journal of Mathematical Analysis and Applications 160, no. 2 (September 1991): 434–45. http://dx.doi.org/10.1016/0022-247x(91)90316-r.

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24

Alzer, Horst. "On some inequalities of Opial-type." Archiv der Mathematik 63, no. 5 (November 1994): 431–36. http://dx.doi.org/10.1007/bf01196673.

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25

Saker, S. H., D. M. Abdou, and I. Kubiaczyk. "Opial and Pólya Type Inequalities Via Convexity." Fasciculi Mathematici 60, no. 1 (June 1, 2018): 145–59. http://dx.doi.org/10.1515/fascmath-2018-0009.

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Abstract In this paper, we prove some new dynamic inequalities related to Opial and Pólya type inequalities on a time scale 𝕋. We will derive the integral and discrete inequalities of Pólya’s type as special cases and also derive several classical integral inequalities of Opial’s type that has been obtained in the literature as special cases. The main results will be proved by using the chain rule, Hölder’s inequality and Jensen’s inequality, Taylor formula on time scales.

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26

Anastassiou, George A. "Complex left Caputo fractional inequalities." Studia Universitatis Babes-Bolyai Matematica 66, no. 2 (June 15, 2021): 329–38. http://dx.doi.org/10.24193/subbmath.2021.2.09.

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27

Saker, S. H. "Some Opial-Type Inequalities on Time Scales." Abstract and Applied Analysis 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/265316.

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We will prove some dynamic inequalities of Opial type on time scales which not only extend some results in the literature but also improve some of them. Some discrete inequalities are derived from the main results as special cases.

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28

PACHPATTE, B. G. "OPIAL TYPE DISCRETE INEQUALITIES IN TWO VARIABLES." Tamkang Journal of Mathematics 22, no. 4 (December 1, 1991): 323–28. http://dx.doi.org/10.5556/j.tkjm.22.1991.4616.

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The aim of the present note is to establish two new discrete inequalities of the Opial type involving functions of two variables and their differences. The analysis used in the proofs is elementary and the results established, provide new estimates on these types of inequalities.

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29

Budak, Hüseyin. "Opial type inequalities for double Riemann-Stieltjes integrals." Moroccan Journal of Pure and Applied Analysis 4, no. 2 (December 1, 2018): 111–21. http://dx.doi.org/10.1515/mjpaa-2018-0011.

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AbstractIn this paper, we establish some Opial type inequalities for Riemann-Stieltjes integrals of functions with two variables. The obtained inequalities generalize those previously demonstrated (see [2])

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30

Zhao, Chang-Jian, and Wing-Sum Cheung. "ON OPIAL INEQUALITIES INVOLVING HIGHER ORDER DERIVATIVES." Bulletin of the Korean Mathematical Society 49, no. 6 (November 30, 2012): 1263–74. http://dx.doi.org/10.4134/bkms.2012.49.6.1263.

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31

Farid, Ghulam, and Josip Pečarić. "Opial type integral inequalities for fractional derivatives." Fractional Differential Calculus, no. 1 (2012): 31–54. http://dx.doi.org/10.7153/fdc-02-03.

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32

Kuchta, Małgorzata. "Some quadratic integral inequalities of Opial type." Annales Polonici Mathematici 63, no. 2 (1996): 103–13. http://dx.doi.org/10.4064/ap-63-2-103-113.

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33

Sarikaya, Mehmet Zeki, and Hüseyin Budak. "Opial-type inequalities for conformable fractional integrals." Journal of Applied Analysis 25, no. 2 (December 1, 2019): 155–63. http://dx.doi.org/10.1515/jaa-2019-0016.

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Abstract In this paper, we establish the Opial-type inequalities for a conformable fractional integral and give some results in special cases of α. The results presented here would provide generalizations of those given in earlier works.

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34

Agarwal, R. P., and P. Y. H. Pang. "Opial-Type Inequalities Involving Higher Order Derivatives." Journal of Mathematical Analysis and Applications 189, no. 1 (January 1995): 85–103. http://dx.doi.org/10.1006/jmaa.1995.1005.

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35

Agarwal, Ravi P., and Petr Y. H. Pang. "Sharp opial-type inequalities in two variables." Applicable Analysis 56, no. 3-4 (April 1995): 227–42. http://dx.doi.org/10.1080/00036819508840324.

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36

Cheung, Wing-Sum. "On Opial-type inequalities in two variables." Aequationes Mathematicae 38, no. 2-3 (June 1989): 236–44. http://dx.doi.org/10.1007/bf01840008.

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37

Zhao, Chang-Jian, and Wing-Sum Cheung. "On Opial-type integral inequalities and applications." Mathematical Inequalities & Applications, no. 1 (2014): 223–32. http://dx.doi.org/10.7153/mia-17-17.

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38

Anastassiou, George A. "Opial type inequalities for linear differential operators." Mathematical Inequalities & Applications, no. 2 (1998): 193–200. http://dx.doi.org/10.7153/mia-01-17.

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39

Florkiewicz, Bronisław. "On some integral inequalities of Opial type." Mathematical Inequalities & Applications, no. 4 (2000): 485–96. http://dx.doi.org/10.7153/mia-03-47.

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40

Costa, T. M., H. Román-Flores, and Y. Chalco-Cano. "Opial-type inequalities for interval-valued functions." Fuzzy Sets and Systems 358 (March 2019): 48–63. http://dx.doi.org/10.1016/j.fss.2018.04.012.

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41

Agarwal, R. P., and P. Y. H. Pang. "Opial-type inequalities involving higher order differences." Mathematical and Computer Modelling 21, no. 5 (March 1995): 49–69. http://dx.doi.org/10.1016/0895-7177(95)00013-r.

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42

PACHPATTE, B. G. "A NOTE ON GENERALIZED OPIAL TYPE INEQUALITIES." Tamkang Journal of Mathematics 24, no. 2 (June 1, 1993): 229–35. http://dx.doi.org/10.5556/j.tkjm.24.1993.4494.

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In the present note we establish some new inequalities involv- ing integrals of functions and their derivatives which in the special cases yield the well known Opial inequality and some of its generalizations.

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43

Nazeer, Waqas, Ghulam Farid, Zabidin Salleh, and Ayesha Bibi. "On Opial-Type Inequalities for Superquadratic Functions and Applications in Fractional Calculus." Mathematical Problems in Engineering 2021 (June 29, 2021): 1–11. http://dx.doi.org/10.1155/2021/6379883.

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We have studied the Opial-type inequalities for superquadratic functions proved for arbitrary kernels. These are estimated by applying mean value theorems. Furthermore, by analyzing specific functions, the fractional integral and fractional derivative inequalities are obtained.

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44

Pachpatte, B. G. "Inequalities of Opial type in three independent variables." Tamkang Journal of Mathematics 35, no. 2 (June 30, 2004): 145–58. http://dx.doi.org/10.5556/j.tkjm.35.2004.216.

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The aim of the present paper is to establish some new integral inequalities of Opial type involving functions of three independent variables and their partial derivatives. Our results yields in the special cases some of the inequalities recently appeared in the literature.

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45

程, 光一. "A Kind of Dynamic Opial-Type Inequalities on Time Scales." Advances in Applied Mathematics 09, no. 06 (2020): 965–71. http://dx.doi.org/10.12677/aam.2020.96114.

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46

Thanh Duc, Dinh, Nguyen Du Vi Nhan, and Nguyen Tong Xuan. "Inequalities for Partial Derivatives and their Applications." Canadian Mathematical Bulletin 58, no. 3 (September 1, 2015): 486–96. http://dx.doi.org/10.4153/cmb-2015-020-6.

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AbstractWe present various weighted integral inequalities for partial derivatives acting on products and compositions of functions that are applied in order to establish some new Opial-type inequalities involving functions of several independent variables. We also demonstrate the usefulness of our results in the field of partial differential equations.

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47

Yang, Gou-Sheng, and Tien-Shou Huang. "On some inequalities related to Opial-Type inequality in two variables." Tamkang Journal of Mathematics 33, no. 4 (December 31, 2002): 379–86. http://dx.doi.org/10.5556/j.tkjm.33.2002.287.

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48

Farid, Ghulam, and Josip Pečarić. "Opial type integral inequalities for fractional derivatives II." Fractional Differential Calculus, no. 2 (2012): 139–55. http://dx.doi.org/10.7153/fdc-02-11.

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49

Srivastava, H. M., Kuei-Lin Tseng, Shio-Jenn Tseng, and Jen-Chieh Lo. "SOME WEIGHTED OPIAL-TYPE INEQUALITIES ON TIME SCALES." Taiwanese Journal of Mathematics 14, no. 1 (February 2010): 107–22. http://dx.doi.org/10.11650/twjm/1500405730.

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50

Anastassiou, George A., and J. Pečarić. "General Weighted Opial Inequalities for Linear Differential Operators." Journal of Mathematical Analysis and Applications 239, no. 2 (November 1999): 402–18. http://dx.doi.org/10.1006/jmaa.1999.6573.

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