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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)
  • Received : 2020.02.27
  • Accepted : 2020.11.05
  • Published : 2020.12.30

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

References

  1. R.P. Agarwal and P. Y. H. Pang, Sharp opial-type inequalities in two variables, Appl Anal. 56 (3) (1996), 227-242. https://doi.org/10.1080/00036819508840324
  2. H. Budak and Sarikaya, Refinements of Opial type inequalities in two variables, ResearchGate Article: www.researchgate.net/publication/329091454.
  3. H. Budak, Generalizations of Opial type inequalities in two variables using pnorms, Transylvanian Journal of Mathematics and Mechanics, 11 (1-2) (2019), 63-75.
  4. Z. Changjian, and W. Cheung, On improvements of Opial-type inequalities, Georgian Mathematical Journal, 21 (4) (2014), 415-419.
  5. W.S. Cheung, Some new Opial-type inequalities, Mathematika 37 (1990), 136-142. https://doi.org/10.1112/S0025579300012869
  6. W.S. Cheung, Some generalized Opial-type inequalities, J. Math. Anal. Appl. 162 (1991), 317-321. https://doi.org/10.1016/0022-247x(91)90152-p
  7. W.S. Cheung, On Opial-type inequalities in two variables, Aequationes Mathematicae 38 (1989), 236-244. https://doi.org/10.1007/BF01840008
  8. W.S. Cheung, Opial-type inequalities with m functions in n variables, Mathematika 39 (2) (1992), 319-326. https://doi.org/10.1112/S0025579300015047
  9. S. S. Dragomir, Generalizations of Opialis inequalities for two functions and applications, Preprint RGMIA Res. Rep. Coll. 21 (2018), Art. 64.
  10. C. T. Lin and G. S.Yang, A generalized Opial's inequality in two variables, Tamkang J. Math. 15 (1984), 115-122.
  11. Z. Opial, Sur une inegaliti, Ann. Polon. Math. 8 (1960), 29-32. https://doi.org/10.4064/ap-8-1-29-32
  12. B. G. Pachpatte, On Opial-type integral inequalities, J. Math. Anal. Appl. 120 (1986), 547-556. https://doi.org/10.1016/0022-247X(86)90176-9
  13. B. G. Pachpatte, Some inequalities similar to Opial's inequality, Demonstratio Math. 26 (1993), 643-647.
  14. B. G. Pachpatte, A note on some new Opial type integral inequalities, Octogon Math. Mag. 7 (1999), 80-84.
  15. B. G. Pachpatte, On some inequalities of the Weyl type, An. Stiint. Univ. "Al.I. Cuza" Iasi 40 (1994), 89-95.
  16. B. G. Pachpatte, On Opial type integral inequalities, J. Math. Analy. Appl. 120, 547-556 (1986). https://doi.org/10.1016/0022-247X(86)90176-9
  17. B. G. Pachpatte, On two inequalities similar to Opial's inequality in two independent variables, Periodica Math. Hungarica 18 (1987), 137-141. https://doi.org/10.1007/BF01896288
  18. B. G. Pachpatte, On an inequality of opial type in two variables, Indian J. Pure Appl. Math. 23 (9) (1992), 657-661.
  19. B.C. Pachpatte, On two independent variable Opial-type integral inequalities, J. Math. Anal. Appl. 125 (1987), 47-57. https://doi.org/10.1016/0022-247x(87)90163-6
  20. B.C. Pachpatte, On Opial type inequalities in two independent variables, Proc. Royal Soc. Edinburgh, 100A (1985), 263-270. https://doi.org/10.1017/S0308210500013809
  21. B.C. Pachpatte, On certain two dimensional integral inequalities, Chinese J. Math. 17 (4) (1989), 273-279.
  22. B.C. Pachpatte, On multidimensional Opial-type inequalities, J. Math. Anal. Appl. 126 (1) (1987), 85-89. https://doi.org/10.1016/0022-247x(87)90076-x
  23. B.C. Pachpatte, On some new integral inequalities in ceveral independent variables, Chinese Journal of Mathematics 14 (2) (1986), 69-79.
  24. B.C. Pachpatte, Inequalities of Opial type in three independent variables, Tamkang Journal of Mathematics 35 (2) (2004), 145-158. https://doi.org/10.5556/j.tkjm.35.2004.216
  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. https://doi.org/10.11650/twjm/1500405730
  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.