Inequalities of Hardy Type via Superquadratic Functions with General Kernels and Measures for Several Variables on Time Scales. (23rd October 2020)

• Record Type: Journal Article
• Authors: Rezk, H. M.; Abd El-Hamid, H. A.; Ahmed, A. M.; AlNemer, Ghada; Zakarya, M.
• Other Names: Sooppy Nisar Kottakkaran Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-10-23
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/6427378
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We use the properties of superquadratic functions to produce various improvements and popularizations on time scales of the Hardy form inequalities and their converses. Also, we include various examples and interpretations of the disparities in the literature that exist. In particular, our findings can be seen as refinements of some recent results closely linked to the time-scale inequalities of the classical Hardy, Pólya-Knopp, and Hardy-Hilbert. Some continuous inequalities are derived from the main results as special cases. The essential results will be proved by making use of some algebraic inequalities such as the Minkowski inequality, the refined Jensen inequality, and the Bernoulli inequality on time scales.