scholarly journals Hardy-type inequalities for means

2004 ◽  
Vol 70 (3) ◽  
pp. 521-528 ◽  
Author(s):  
Zsolt Páles ◽  
Lars-Erik Persson
Keyword(s):  
Sufficient Conditions ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Finite Constant

In this paper we consider inequalities of the form , Where M is a mean. The main results of the paper offer sufficient conditions on M so that the above inequality holds with a finite constant C. The results obtained extend Hardy's and Carleman's classical inequalities together with their various generalisations in a new dirction.

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 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

On some Hardy-type inequalities for fractional calculus operators

2017 ◽  
Vol 11 (2) ◽  
pp. 438-457 ◽  
Author(s):  
Sajid Iqbal ◽  
Josip Pečarić ◽  
Muhammad Samraiz ◽  
Zivorad Tomovski
Keyword(s):  
Fractional Calculus ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Fractional Calculus Operators

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.

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