On a Strengthened Form of a General Hardy-Type Inequality (original) (raw)

Refinements of some limit Hardy-type inequalities via superquadracity

Publications de l'Institut Math?matique (Belgrade), 2017

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.

Some Hardy-Type Inequalities for Superquadratic Functions via Delta Fractional Integrals

Mathematical Problems in Engineering

In this paper, Jensen and Hardy inequalities, including Pólya–Knopp type inequalities for superquadratic functions, are extended using Riemann–Liouville delta fractional integrals. Furthermore, some inequalities are proved by using special kernels. Particular cases of obtained inequalities give us the results on time scales calculus, fractional calculus, discrete fractional calculus, and quantum fractional calculus.

Refined multidimensional Hardy-type inequalities via superquadracity

Some new refined multidimensional Hardy-type inequalities for p ≥ 2 and their duals are derived and discussed. Moreover, these inequalities hold in the reversed direction when 1 < p ≤ 2. The results obtained are based mainly on some new results for superquadratic and subquadratic functions. In particular, our results further extend the recent results in [

Hardy type inequalities for superquadratic functions via Jackson Nörlund integrals

Journal of Mathematics and Computer Science

In this paper, it is tried to describe Hardy-type inequalities with certain kernels by using Jackson Nörlund integrals. In order to obtain the desired Hardy type inequalities, firstly, we prove Jensen's inequality involving super quadratic function and Jackson Nörlund integrals. Further, we discuss Hardy-type inequalities by choosing special kernels. Polya-Knopp type inequalities are also deduced to find applications.

Opial-type inequalities for superquadratic functions

Filomat, 2022

In this paper we prove new Opial-type inequalities for arbitrary kernels using superquadratic functions, also their extensions are obtained. Furthermore, we find their fractional versions by applying different kinds of fractional integral and fractional derivative operators.

Some higher order Hardy inequalities

Journal of Inequalities and Applications, 2012

We investigate the k-th order Hardy inequality (1.1) for functions satisfying rather general boundary conditions (1.2), show which of these conditions are admissible and derive sufficient, and necessary and sufficient, conditions (for 0 < q < ∞, p > 1) on u, v for (1.1) to hold.

On Some Integral Inequalities of Hardy-Type Operators

Advances in Pure Mathematics, 2013

In recent time, hardy integral inequalities have received attentions of many researchers. The aim of this paper is to obtain new integral inequalities of hardy-type which complement some recent results.

On weighted Hardy-type inequalities

Mathematical Inequalities & Applications, 2020

We revisit weighted Hardy-type inequalities employing an elementary ad hoc approach that yields explicit constants. We also discuss the infinite sequence of power weighted Birman-Hardy-Rellich-type inequalities and derive an operator-valued version thereof.