New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations. (1st August 2019)

• Record Type: Journal Article
• Authors: Saker, S. H.; Sayed, A. G.; Sikorska-Nowak, A.; Abohela, I.
• Other Names: Rehak Pavel Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2019(2019)
• Publication Date: 2019-08-01
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2019/6757080
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : 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.