Refinement Multidimensional Dynamic Inequalities With General Kernels and Measures
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Abstract
Using the properties of superquadratic and subquadratic functions, we establish some new refinement multidimensional dynamic inequalities of Hardy's type on time scales. Our results contain some of the recent results related to classical multidimensional Hardy's and Polya-Knopp's inequalities on time scales. To show motivation of the paper, we apply our results to obtain some particular multidimensional cases and provide refinements of some Hardy-type inequalities known in the literature.
Description
Rezk, H. M./0000-0001-6782-7908
ORCID
Keywords
Hardy-Type Inequality, Polya-Knopp-Type Inequalities, Superquadratic (Subquadratic) Functions, Hardy'S Integral Operator With Kernel, Time Scales, Hardy’s Integral Operator with Kernel, Pólya–Knopp-Type Inequalities, Hardy’s integral operator with kernel, Matrix Inequalities and Geometric Means, Integro-Differential Equations, Theory and Applications of Fractional Differential Equations, Mathematical analysis, QA1-939, FOS: Mathematics, Biology, Ecology, Applied Mathematics, FOS: Clinical medicine, Pure mathematics, Hardy-type inequality, Time scales, Applied mathematics, Nonlocal Partial Differential Equations and Boundary Value Problems, Superquadratic (subquadratic) functions, Inequality, FOS: Biological sciences, Dentistry, Physical Sciences, Pólya–Knopp-type inequalities, Medicine, Calculus (dental), Type (biology), Mathematics, superquadratic functions, Pólya-Knopp-type inequalities, Convexity of real functions in one variable, generalizations, Hardy integral operator, Other analytical inequalities, Real analysis on time scales or measure chains, time scales, Inequalities involving derivatives and differential and integral operators, Inequalities for sums, series and integrals
Fields of Science
01 natural sciences, 0101 mathematics
Citation
Saker, Samir H...et al. (2019). "Refinement multidimensional dynamic inequalities with general kernels and measures", Journal of Inequalities and Applications, Vol. 2019, No. 1.
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15
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2019
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1
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19
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