scholarly journals Generalizations of Hardy Type Inequalities by Abel–Gontscharoff’s Interpolating Polynomial

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1724
Author(s):  
Kristina Krulić Himmelreich ◽  
Josip Pečarić ◽  
Dora Pokaz ◽  
Marjan Praljak
Keyword(s):  
Convex Functions ◽  
Upper Bounds ◽  
Higher Order ◽  
Hardy’S Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Hardy's Inequality

In this paper, we extend Hardy’s type inequalities to convex functions of higher order. Upper bounds for the generalized Hardy’s inequality are given with some applications.

Hardy Inequalities on the Real Line

2011 ◽  
Vol 54 (1) ◽  
pp. 159-171 ◽  
Author(s):  
Mohammad Sababheh
Keyword(s):  
Real Line ◽  
Hardy’S Inequality ◽  
Hardy Inequalities ◽  
The Real ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Hardy's Inequality ◽  
Littlewood Conjecture ◽  
The Relationship

AbstractWe prove that some inequalities, which are considered to be generalizations of Hardy's inequality on the circle, can be modified and proved to be true for functions integrable on the real line. In fact we would like to show that some constructions that were used to prove the Littlewood conjecture can be used similarly to produce real Hardy-type inequalities. This discussion will lead to many questions concerning the relationship between Hardy-type inequalities on the circle and those on the real line.

On a new class of Hardy type inequalities

1987 ◽  
Vol 105 (1) ◽  
pp. 265-274 ◽  
Author(s):  
B.G. Pachpatte
Keyword(s):  
Integral Inequalities ◽  
Hardy’S Inequality ◽  
Hardy Type Inequalities ◽  
New Class ◽  
Hardy Type ◽  
Hardy's Inequality

SynopsisIn this paper we establish a new class of integral inequalities which originate from the well-known Hardy's inequality. The analysis used in the proofs is quite elementary and is based on the idea used by Levinson to obtain generalisations of Hardy's inequality.

A New Approach to the Sawyer and Sinnamon Characterizations of Hardy's Inequality for Decreasing Functions

2008 ◽  
Vol 15 (2) ◽  
pp. 295-306
Author(s):  
Maria Johansson ◽  
Lars-Erik Persson ◽  
Anna Wedestig
Keyword(s):  
Hardy’S Inequality ◽  
New Approach ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Hardy's Inequality ◽  
Decreasing Functions

Abstract Some Hardy type inequalities for decreasing functions are characterized by one condition (Sinnamon), while others are described by two independent conditions (Sawyer). In this paper we make a new approach to deriving such results and prove a theorem, which covers both the Sinnamon result and the Sawyer result for the case where one weight is increasing. In all cases we point out that the characterizing condition is not unique and can even be chosen among some (infinite) scales of conditions.

scholarly journals Hardy-Type Inequalities for an Extension of the Riemann- Liouville Fractional Derivative Operators

2021 ◽  
Vol 45 (5) ◽  
pp. 797-813
Author(s):  
SAJID IQBAL ◽  
◽  
GHULAM FARID ◽  
JOSIP PEČARIĆ ◽  
ARTION KASHURI
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Mean Value ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Liouville Fractional Derivative ◽  
Fractional Derivative Operators

In this paper we present variety of Hardy-type inequalities and their refinements for an extension of Riemann-Liouville fractional derivative operators. Moreover, we use an extension of extended Riemann-Liouville fractional derivative and modified extension of Riemann-Liouville fractional derivative using convex and monotone convex functions. Furthermore, mean value theorems and n-exponential convexity of the related functionals is discussed.

On Some Integral Inequalities Related to Hardy's

1977 ◽  
Vol 20 (3) ◽  
pp. 307-312 ◽  
Author(s):  
Christopher Olutunde Imoru
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Integral Inequalities ◽  
Hardy’S Inequality ◽  
Jensen's Inequality ◽  
Hardy's Inequality ◽  
Special Case

AbstractWe obtain mainly by using Jensen's inequality for convex functions an integral inequality, which contains as a special case Shun's generalization of Hardy's inequality.

scholarly journals Weighted Hardy-type inequalities for monotone convex functions with some applications

2013 ◽  
pp. 31-53 ◽  
Author(s):  
Sajid Iqbal ◽  
Kristina Krulić Himm lreich ◽  
Josip Pečarić
Keyword(s):  
Convex Functions ◽  
Hardy Type Inequalities ◽  
Hardy Type

scholarly journals Hardy-Type Inequalities on Time Scale via Convexity in Several Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tzanko Donchev ◽  
Ammara Nosheen ◽  
Josip Pečarić
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Time Scale ◽  
Hardy Type Inequalities ◽  
Arbitrary Time ◽  
Hardy Type ◽  
Several Variables ◽  
New Inequalities

We extend some Hardy-type inequalities with general kernels to arbitrary time scales using multivariable convex functions. Some classical and new inequalities are deduced seeking applications.

scholarly journals Characterizations of weighted dynamic Hardy-type inequalities with higher-order derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
R. R. Mahmoud ◽  
K. R. Abdo
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Type Inequality ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Hardy Type Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Weighted Functions ◽  
Necessary And Sufficient

AbstractIn this paper, we establish some necessary and sufficient conditions for the validity of a generalized dynamic Hardy-type inequality with higher-order derivatives with two different weighted functions on time scales. The corresponding continuous and discrete cases are captured when $\mathbb{T=R}$ T = R and $\mathbb{T=N}$ T = N , respectively. Finally, some applications to our main result are added to conclude some continuous results known in the literature and some other discrete results which are essentially new.

scholarly journals SOME HARDY-TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA DELTA FRACTIONAL INTEGRALS

Fractals ◽  
2021 ◽  
pp. 2240004
Author(s):  
FUZHANG WANG ◽  
USAMA HANIF ◽  
AMMARA NOSHEEN ◽  
KHURAM ALI KHAN ◽  
HIJAZ AHMAD ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Time Scales ◽  
Convex Functions ◽  
Type Inequality ◽  
Fractional Integrals ◽  
Discrete Fractional Calculus ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Hilbert Type

In this paper, some Jensen- and Hardy-type inequalities for convex functions are extended by using Riemann–Liouville delta fractional integrals. Further, some Pólya–Knopp-type inequalities and Hardy–Hilbert-type inequality for convex functions are also proved. Moreover, some related inequalities are proved by using special kernels. Particular cases of resulting inequalities provide the results on fractional calculus, time scales calculus, quantum fractional calculus and discrete fractional calculus.

scholarly journals Generalized sharp Hardy type and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds

2009 ◽  
Vol 40 (4) ◽  
pp. 401-413 ◽  
Author(s):  
Shihshu Walter Wei ◽  
Ye Li
Keyword(s):  
Fixed Point ◽  
Euclidean Space ◽  
Riemannian Manifolds ◽  
Compact Support ◽  
Hardy’S Inequality ◽  
Sharp Constants ◽  
Hardy Type ◽  
Hardy's Inequality ◽  
Nirenberg Inequality

We prove generalized Hardy's type inequalities with sharp constants and Caffarelli-Kohn-Nirenberg inequalities with sharp constants on Riemannian manifolds $M$. When the manifold is Euclidean space we recapture the sharp Caffarelli-Kohn-Nirenberg inequality. By using a double limiting argument, we obtain an inequality that implies a sharp Hardy's inequality, for functions with compact support on the manifold $M $ (that is, not necessarily on a punctured manifold $ M \backslash \{ x_0 \} $ where $x_0$ is a fixed point in $M$). Some topological and geometric applications are discussed.

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