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 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.

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 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 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.

scholarly journals Some new Hardy-type inequalities on time scales

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ahmed A. El-Deeb ◽  
Hamza A. Elsennary ◽  
Dumitru Baleanu
Keyword(s):  
Time Scales ◽  
Hardy Type Inequalities ◽  
Hardy Type

On Hardy-Type Inequalities

1998 ◽  
Vol 194 (1) ◽  
pp. 23-33 ◽  
Author(s):  
D. E. Edmunds ◽  
R. Hurri-Syrjänen
Keyword(s):  
Hardy Type Inequalities ◽  
Hardy Type
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