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Refinements of some limit hardy-Type Inequalities via Superquadracity
(Journal article; Tidsskriftartikkel; Peer reviewed, 2017-11-03)
Refinements of some limit Hardy-type inequalities are derived and discussed using the concept of superquadracity. We also proved that all three constants appearing in the refined inequalities obtained are sharp. The natural turning point of our refined Hardy inequality is p=2 and for this case we have even equality.
Multidimensional Hardy-type inequalities on time scales with variable exponents
(Journal article; Peer reviewed, 2019)
A new Jensen inequality for multivariate superquadratic functions is derived and proved. The derived Jensen inequality is then employed to obtain the general Hardy-type integral inequality for superquadratic and subquadratic functions of several variables.