Browse > Article
http://dx.doi.org/10.11568/kjm.2020.28.4.717

ON WEIGHTED GENERALIZATION OF OPIAL TYPE INEQUALITIES IN TWO VARIABLES  

Budak, Huseyin (Department of Mathematics Faculty of Science and Arts Duzce University)
Sarikaya, Mehmet Zeki (Department of Mathematics Faculty of Science and Arts Duzce University)
Kashuri, Artion (Department of Mathematics Faculty of Technical Science University Ismail Qemali)
Publication Information
Korean Journal of Mathematics / v.28, no.4, 2020 , pp. 717-737 More about this Journal
Abstract
In this paper, we establish some weighted generalization of Opial type inequalities in two independent variables for two functions. We also obtain weighted Opial type inequalities by using p-norms. Special cases of our results reduce to the inequalities in earlier study.
Keywords
Opial inequality; $H{\ddot{o}}lder^{\prime}s$ inequality;
Citations & Related Records
연도 인용수 순위
  • Reference
1 H. Budak, Generalizations of Opial type inequalities in two variables using pnorms, Transylvanian Journal of Mathematics and Mechanics, 11 (1-2) (2019), 63-75.
2 Z. Changjian, and W. Cheung, On improvements of Opial-type inequalities, Georgian Mathematical Journal, 21 (4) (2014), 415-419.
3 W.S. Cheung, Some new Opial-type inequalities, Mathematika 37 (1990), 136-142.   DOI
4 W.S. Cheung, Some generalized Opial-type inequalities, J. Math. Anal. Appl. 162 (1991), 317-321.   DOI
5 W.S. Cheung, On Opial-type inequalities in two variables, Aequationes Mathematicae 38 (1989), 236-244.   DOI
6 W.S. Cheung, Opial-type inequalities with m functions in n variables, Mathematika 39 (2) (1992), 319-326.   DOI
7 S. S. Dragomir, Generalizations of Opialis inequalities for two functions and applications, Preprint RGMIA Res. Rep. Coll. 21 (2018), Art. 64.
8 C. T. Lin and G. S.Yang, A generalized Opial's inequality in two variables, Tamkang J. Math. 15 (1984), 115-122.
9 B. G. Pachpatte, On Opial-type integral inequalities, J. Math. Anal. Appl. 120 (1986), 547-556.   DOI
10 Z. Opial, Sur une inegaliti, Ann. Polon. Math. 8 (1960), 29-32.   DOI
11 B. G. Pachpatte, Some inequalities similar to Opial's inequality, Demonstratio Math. 26 (1993), 643-647.
12 B. G. Pachpatte, A note on some new Opial type integral inequalities, Octogon Math. Mag. 7 (1999), 80-84.
13 B. G. Pachpatte, On some inequalities of the Weyl type, An. Stiint. Univ. "Al.I. Cuza" Iasi 40 (1994), 89-95.
14 B. G. Pachpatte, On Opial type integral inequalities, J. Math. Analy. Appl. 120, 547-556 (1986).   DOI
15 B. G. Pachpatte, On two inequalities similar to Opial's inequality in two independent variables, Periodica Math. Hungarica 18 (1987), 137-141.   DOI
16 B. G. Pachpatte, On an inequality of opial type in two variables, Indian J. Pure Appl. Math. 23 (9) (1992), 657-661.
17 B.C. Pachpatte, On two independent variable Opial-type integral inequalities, J. Math. Anal. Appl. 125 (1987), 47-57.   DOI
18 R.P. Agarwal and P. Y. H. Pang, Sharp opial-type inequalities in two variables, Appl Anal. 56 (3) (1996), 227-242.   DOI
19 B.C. Pachpatte, On Opial type inequalities in two independent variables, Proc. Royal Soc. Edinburgh, 100A (1985), 263-270.   DOI
20 H. Budak and Sarikaya, Refinements of Opial type inequalities in two variables, ResearchGate Article: www.researchgate.net/publication/329091454.
21 B.C. Pachpatte, Inequalities of Opial type in three independent variables, Tamkang Journal of Mathematics 35 (2) (2004), 145-158.   DOI
22 B.C. Pachpatte, On certain two dimensional integral inequalities, Chinese J. Math. 17 (4) (1989), 273-279.
23 B.C. Pachpatte, On multidimensional Opial-type inequalities, J. Math. Anal. Appl. 126 (1) (1987), 85-89.   DOI
24 B.C. Pachpatte, On some new integral inequalities in ceveral independent variables, Chinese Journal of Mathematics 14 (2) (1986), 69-79.
25 H. M. Srivastava, K.-L. Tseng, S.-J. Tseng and J.-C. Lo, Some weighted Opialtype inequalities on time scales, Taiwanese J. Math. 14 (2010), 107-122.   DOI
26 J. Traple, On a boundary value problem for systems of ordinary differential equations of second order, Zeszyty Nauk. Univ. Jagiello. Prace Mat. 15 (1971), 159-168.
27 C.-J. Zhao and W.-S. Cheung, On Opial-type integral inequalities and applications, Math. Inequal. Appl. 17 (1) (2014), 223-232.
28 G. S. Yang. Inequality of Opial-type in two variables, Tamkang J. Math. 13 (1982), 255-259.