scholarly journals Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2964
Author(s):  
Ahmed A. El-Deeb ◽  
Jan Awrejcewicz
Keyword(s):  
Present Article ◽  
Time Scales ◽  
Jensen’S Inequality ◽  
Legendre Transform ◽  
Jensen's Inequality ◽  
Discrete Inequalities ◽  
Special Case ◽  
Hilbert Type

The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert type on time scales. We present and prove very important generalized results with the help of Fenchel–Legendre transform, submultiplicative functions. We prove the (γ,a)-nabla conformable Hölder’s and Jensen’s inequality on time scales. We prove several inequalities due to Hardy–Hilbert inequalities on time scales. Furthermore, we introduce the continuous inequalities and discrete inequalities as special case.

scholarly journals Some Dynamic Inequalities of Hilbert’s Type

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
A. M. Ahmed ◽  
Ghada AlNemer ◽  
M. Zakarya ◽  
H. M. Rezk
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Hölder's Inequality ◽  
Discrete Inequalities ◽  
Special Case ◽  
Hilbert Type

This paper is concerned with deriving some new dynamic Hilbert-type inequalities on time scales. The basic idea in proving the results is using some algebraic inequalities, Hölder’s inequality and Jensen’s inequality, on time scales. As a special case of our results, we will obtain some integrals and their corresponding discrete inequalities of Hilbert’s type.

scholarly journals New dynamic Hilbert-type inequalities in two independent variables involving Fenchel–Legendre transform

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
A. A. El-Deeb ◽  
Saima Rashid ◽  
Zareen A. Khan ◽  
S. D. Makharesh
Keyword(s):  
Time Scales ◽  
Legendre Transform ◽  
Independent Variables ◽  
Hilbert Type ◽  
Two Independent Variables ◽  
New Inequalities

AbstractIn this paper, we establish some dynamic Hilbert-type inequalities in two independent variables on time scales by using the Fenchel–Legendre transform. We also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as particular cases. Our results give more general forms of several previously established inequalities.

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 Some Dynamic Hilbert-Type Inequalities on Time Scales

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1410 ◽  
Author(s):  
Ghada AlNemer ◽  
Mohammed Zakarya ◽  
Hoda A. Abd El-Hamid ◽  
Praveen Agarwal ◽  
Haytham M. Rezk
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Discrete Inequalities ◽  
Hilbert Type ◽  
General Time

Throughout this article, we will demonstrate some new generalizations of dynamic Hilbert type inequalities, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. From these inequalities, as particular cases, we formulate some integral and discrete inequalities that have been demonstrated in the literature and also extend some of the dynamic inequalities that have been achieved in time scales.

scholarly journals Some dynamic Hilbert-type inequalities for two variables on time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
H. A. Abd El-Hamid ◽  
H. M. Rezk ◽  
A. M. Ahmed ◽  
Ghada AlNemer ◽  
M. Zakarya ◽  
...  
Keyword(s):  
Time Scales ◽  
Special Cases ◽  
Discrete Inequalities ◽  
Hilbert Type

AbstractIn this paper, we discuss some new Hilbert-type dynamic inequalities on time scales in two separate variables. We also deduce special cases, like some integral and their respective discrete inequalities.

scholarly journals Estimation of divergence measures via weighted Jensen inequality on time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Iqrar Ansari ◽  
Khuram Ali Khan ◽  
Ammara Nosheen ◽  
Ðilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Time Scales ◽  
Lower Bounds ◽  
Time Scale ◽  
Jensen’S Inequality ◽  
Jensen Inequality ◽  
Jensen's Inequality ◽  
Quantum Calculus ◽  
Divergence Measures ◽  
Zipf Law ◽  
New Inequalities

AbstractThe main purpose of the presented paper is to obtain some time scale inequalities for different divergences and distances by using weighted time scales Jensen’s inequality. These results offer new inequalities in h-discrete calculus and quantum calculus and extend some known results in the literature. The lower bounds of some divergence measures are also presented. Moreover, the obtained discrete results are given in the light of the Zipf–Mandelbrot law and the Zipf law.

scholarly journals Opial and Pólya Type Inequalities Via Convexity

2018 ◽  
Vol 60 (1) ◽  
pp. 145-159 ◽  
Author(s):  
S. H. Saker ◽  
D. M. Abdou ◽  
I. Kubiaczyk
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Hölder’S Inequality ◽  
Jensen’S Inequality ◽  
Chain Rule ◽  
Integral Inequalities ◽  
Taylor Formula ◽  
Special Cases ◽  
Discrete Inequalities ◽  
Classical Integral

Abstract In this paper, we prove some new dynamic inequalities related to Opial and Pólya type inequalities on a time scale 𝕋. We will derive the integral and discrete inequalities of Pólya’s type as special cases and also derive several classical integral inequalities of Opial’s type that has been obtained in the literature as special cases. The main results will be proved by using the chain rule, Hölder’s inequality and Jensen’s inequality, Taylor formula on time scales.

scholarly journals Quantile Jensen’s inequalities

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mu Zhao ◽  
Xinai Yang ◽  
Qi He ◽  
Zunrong Zhou ◽  
Xiangyu Ge
Keyword(s):  
Confidence Interval ◽  
Jensen’S Inequality ◽  
Random Variable ◽  
Pivotal Quantity ◽  
Jensen's Inequality ◽  
Rigorous Description ◽  
The Relationship ◽  
Special Case

AbstractQuantiles of random variable are crucial quantities that give more delicate information about distribution than mean and median and so on. We establish Jensen’s inequality for q-quantile ($q\geq 0.5$ q ≥ 0.5 ) of a random variable, which includes as a special case Merkle (Stat. Probab. Lett. 71(3):277–281, 2005) where Jensen’s inequality about median (i.e. $q= 0.5$ q = 0.5 ) was given. We also refine this inequality in the case where $q<0.5$ q < 0.5 . An application to the confidence interval of parameters in pivotal quantity is also considered by virtue of the rigorous description on the relationship between quantiles and intervals that have required probability.

scholarly journals New bounds for soft margin estimator via concavity of Gaussian weighting function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hidayat Ullah ◽  
Muhammad Adil Khan ◽  
Josip Pečarić
Keyword(s):  
Present Article ◽  
Weighting Function ◽  
Jensen’S Inequality ◽  
Network Robustness ◽  
Similarity Function ◽  
Temporal Network ◽  
Jensen's Inequality ◽  
Jaccard Similarity ◽  
Soft Margin

AbstractIn the present article, we elaborate on the notion to obtain bounds for the soft margin estimator of “Identification of Patient Zero in Static and Temporal Network-Robustness and Limitations”. To achieve these bounds for the soft margin estimator, we utilize the concavity of the Gaussian weighting function and well-known Jensen’s inequality. To acquire some more general bounds for the soft margin estimator, we consider some general functions defined on rectangles. We also use the behavior of the Jaccard similarity function to extract some handsome bounds for the soft margin estimator.

scholarly journals Diamond- Jensen's Inequality on Time Scales

2008 ◽  
Vol 2008 (1) ◽  
pp. 576876 ◽  
Author(s):  
MoulayRchid Sidi Ammi ◽  
RuiAC Ferreira ◽  
DelfimFM Torres
Keyword(s):  
Time Scales ◽  
Jensen’S Inequality ◽  
Jensen's Inequality
Sign in / Sign up

Export Citation Format

Share Document