scholarly journals Integral Inequality of Hardy-Type on Time Scales

2019 ◽  
Vol 09 (06) ◽  
pp. 534-543
Author(s):  
Emmanuella Ehui Aribike ◽  
Yisa Oluwatoyin Anthonio ◽  
Kamilu Rauf ◽  
Michael Oyelami Ajisope
Keyword(s):  
Time Scales ◽  
Integral Inequality ◽  
Hardy Type

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

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 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 Properties of Some Partial Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Deepak B. Pachpatte
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Point Theorem ◽  
Integral Inequality ◽  
Dynamic Equation ◽  
Dynamic Equations ◽  
Banach Fixed Point Theorem

The main objective of the paper is to study the properties of the solution of a certain partial dynamic equation on time scales. The tools employed are based on the application of the Banach fixed-point theorem and a certain integral inequality with explicit estimates on time scales.

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.

scholarly journals Some Dynamic Inequalities via Diamond Integrals for Function of Several Variables

2021 ◽  
Vol 5 (4) ◽  
pp. 207
Author(s):  
Muhammad Bilal ◽  
Khuram Ali Khan ◽  
Hijaz Ahmad ◽  
Ammara Nosheen ◽  
Khalid Mahmood Awan ◽  
...  
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Jensen’S Inequality ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Several Variables ◽  
Time Scale Calculus ◽  
Special Cases ◽  
Function Of Several Variables ◽  
New Inequalities

In this paper, Jensen’s inequality and Fubini’s Theorem are extended for the function of several variables via diamond integrals of time scale calculus. These extensions are used to generalize Hardy-type inequalities with general kernels via diamond integrals for the function of several variables. Some Hardy Hilbert and Polya Knop type inequalities are also discussed as special cases. Classical and new inequalities are deduced from the main results using special kernels and particular time scales.

scholarly journals Reverses Hardy-type inequalities via Jensen integral inequality

2021 ◽  
Vol 52 ◽  
pp. 43-51
Author(s):  
Bouharket Benaissa ◽  
Aissa Benguessoum
Keyword(s):  
Weight Function ◽  
Integral Inequality ◽  
Hölder Inequality ◽  
Integral Inequalities ◽  
Hardy Inequalities ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Jensen Integral Inequality ◽  
Number Of Authors

The integral inequalities concerning the inverse Hardy inequalities have been studied by a large number of authors during this century, of these articles have appeared, the work of Sulaiman in 2012, followed by Banyat Sroysang who gave an extension to these inequalities in 2013. In 2020 B. Benaissa presented a generalization of inverse Hardy inequalities. In this article, we establish a new generalization of these inequalities by introducing a weight function and a second parameter. The results will be proved using the Hölder inequality and the Jensen integral inequality. Several the reverses weighted Hardy’s type inequalities and the reverses Hardy’s type inequalities were derived from the main results.

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