Weighted dynamic inequalities of Opial-type on time scales

Advances in Difference Equations

  ^{1    2    2    3} 

[1] 0000 0001 2155 6022, grid.411303.4, Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt;0000 0004 0621 1570, grid.7269.a, Department of Mathematics, Faculty of Women for (Art, Science, and Education), Ain Shams University, Cairo, Egypt;Department of Mathematics, Princess Noura bint Abdulrahman University, Riyadh, Saudi Arabia;

关键词: Opial-type inequality;    Dynamic inequality;    Time scale;    26D10;    26D15;    26E70;    34A40;   

DOI  :  10.1186/s13662-019-2325-8

来源: publisher

【 摘 要 】

In this paper, we will state and prove some weighted dynamic inequalities of Opial-type involving integrals of powers of a function and of its derivative on time scales which not only extend some results in the literature but also improve some of them. The main results will be proved by using some algebraic inequalities, the Hölder inequality and a simple consequence of Keller’s chain rule on time scales. As special cases of the obtained dynamic inequalities, we will get some continuous and discrete inequalities.

【 授权许可】

CC BY