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

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 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 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 Generalized Jensen’s functional on time scales via extended Montgomery identity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sofia Ramzan ◽  
Ammara Nosheen ◽  
Rabia Bibi ◽  
Josip Pečarić
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Montgomery Identity

AbstractIn the paper, we use Jensen’s inequality for diamond integrals and generalize it for n-convex functions with the help of an extended Montgomery identity. Moreover, the bounds have been suggested for identities associated with the generalized Jensen-type functional.

scholarly journals On Hilbert's inequality on time scales

2017 ◽  
Vol 11 (2) ◽  
pp. 399-423 ◽  
Author(s):  
Saker Saker ◽  
A.A. El-Deeb ◽  
H.M. Rezk ◽  
Ravi Agarwal
Keyword(s):  
Time Scales ◽  
Jensen’S Inequality ◽  
Chain Rule ◽  
Simple Consequence ◽  
Jensen's Inequality ◽  
Hilbert’S Inequality ◽  
Special Cases

In this paper, we will prove some new dynamic inequalities of Hilbert's type on time scales. Our results as special cases extend some obtained dynamic inequalities on time scales.and also contain some integral and discrete in- equalities as special cases. We prove our main results by using some algebraic inequalities, H?older's inequality, Jensen's inequality and a simple consequence of Keller's chain rule on time scales.

On a global upper bound for Jensen's inequality

2009 ◽  
Vol 50 ◽  
Author(s):  
Julije Jaksetic ◽  
Bogdan Gavrea ◽  
Josip Pecaric
Keyword(s):  
Upper Bound ◽  
Jensen’S Inequality ◽  
Jensen's Inequality

scholarly journals New refinements of the discrete Jensen’s inequality generated by finite or infinite permutations

2019 ◽  
Vol 94 (6) ◽  
pp. 1109-1121
Author(s):  
László Horváth
Keyword(s):  
Banach Spaces ◽  
Jensen’S Inequality ◽  
Vector Spaces ◽  
Real Vector ◽  
Finite Sets ◽  
Jensen's Inequality

AbstractIn this paper some new refinements of the discrete Jensen’s inequality are obtained in real vector spaces. The idea comes from some former refinements determined by cyclic permutations. We essentially generalize and extend these results by using permutations of finite sets and bijections of the set of positive numbers. We get refinements of the discrete Jensen’s inequality for infinite convex combinations in Banach spaces. Similar results are rare. Finally, some applications are given on different topics.

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