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

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Usama Hanif ◽  
Ammara Nosheen ◽  
Rabia Bibi ◽  
Khuram Ali Khan ◽  
Hamid Reza Moradi
Keyword(s):  
Fractional Calculus ◽  
Time Scales ◽  
Fractional Integrals ◽  
Discrete Fractional Calculus ◽  
Hardy Inequalities ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Superquadratic Functions

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.

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 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 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 Inequalities of Hardy Type via Superquadratic Functions with General Kernels and Measures for Several Variables on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
H. M. Rezk ◽  
H. A. Abd El-Hamid ◽  
A. M. Ahmed ◽  
Ghada AlNemer ◽  
M. Zakarya
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Minkowski Inequality ◽  
Jensen Inequality ◽  
Hardy Type ◽  
Several Variables ◽  
Special Cases ◽  
Superquadratic Functions

We use the properties of superquadratic functions to produce various improvements and popularizations on time scales of the Hardy form inequalities and their converses. Also, we include various examples and interpretations of the disparities in the literature that exist. In particular, our findings can be seen as refinements of some recent results closely linked to the time-scale inequalities of the classical Hardy, Pólya-Knopp, and Hardy-Hilbert. Some continuous inequalities are derived from the main results as special cases. The essential results will be proved by making use of some algebraic inequalities such as the Minkowski inequality, the refined Jensen inequality, and the Bernoulli inequality on time scales.

scholarly journals Bayesian Estimation in Delta and Nabla Discrete Fractional Weibull Distributions

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
M. Ganji ◽  
F. Gharari
Keyword(s):  
Fractional Calculus ◽  
Bayesian Estimation ◽  
Time Scales ◽  
Discrete Distributions ◽  
Weibull Distributions ◽  
Discrete Fractional Calculus

We use discrete fractional calculus for showing the existence of delta and nabla discrete distributions and then apply time scales for definitions of delta and nabla discrete fractional Weibull distributions. Also, we study the Bayesian estimation of the functions of parameters of these distributions.

Anisotropic Hardy inequalities

2017 ◽  
Vol 148 (3) ◽  
pp. 483-498 ◽  
Author(s):  
Francesco Della Pietra ◽  
Giuseppina di Blasio ◽  
Nunzia Gavitone
Keyword(s):  
Distance Function ◽  
Hardy Inequalities ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
General Norm

We study some Hardy-type inequalities involving a general norm in ℝn and an anisotropic distance function to the boundary. The case of the optimality of the constants is also addressed.

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.

scholarly journals Hardy type inequalities on time scales

2015 ◽  
Vol 98 (112) ◽  
pp. 219-226 ◽  
Author(s):  
James Oguntuase
Keyword(s):  
Time Scales ◽  
Hardy Type Inequalities ◽  
Hardy Type

We obtain some new generalizations of Hardy type inequalities involving several functions on time scales. Furthermore, some new multidimensional Hardy-Knopp type inequalities on time scales are derived and discussed.

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