scholarly journals Jensen's Functionals on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Matloob Anwar ◽  
Rabia Bibi ◽  
Martin Bohner ◽  
Josip Pečarić
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Power Means

We consider Jensen’s functionals on time scales and discuss its properties and applications. Further, we define weighted generalized and power means on time scales. By applying the properties of Jensen’s functionals on these means, we obtain several refinements and converses of Hölder’s inequality on time scales.

scholarly journals Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Samir H. Saker
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Higher Order ◽  
Chain Rule ◽  
Simple Consequence ◽  
Hölder's Inequality ◽  
Special Cases ◽  
Discrete Inequalities

We will prove some new Opial dynamic inequalities involving higher order derivatives on time scales. The results will be proved by making use of Hölder's inequality, a simple consequence of Keller's chain rule and Taylor monomials on time scales. Some continuous and discrete inequalities will be derived from our results as special cases.

scholarly journals Consensus of classical and fractional inequalities having congruity on time scale calculus

2019 ◽  
Vol 27 (1) ◽  
pp. 57-69
Author(s):  
Muhammad Jibril Shahab Sahir
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Hölder’S Inequality ◽  
Fractional Integrals ◽  
Power Mean ◽  
Extended Form ◽  
Hölder's Inequality ◽  
Time Scale Calculus ◽  
Power Mean Inequality ◽  
Radon’S Inequality

Abstract In this paper, we find accordance of some classical inequalities and fractional dynamic inequalities. We find inequalities such as Radon’s inequality, Bergström’s inequality, Rogers-Hölder’s inequality, Cauchy-Schwarz’s inequality, the weighted power mean inequality and Schlömilch’s inequality in generalized and extended form by using the Riemann-Liouville fractional integrals on time scales.

scholarly journals A New Reversed Version of a Generalized Sharp Hölder's Inequality and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jingfeng Tian ◽  
Xi-Mei Hu
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Type Inequality ◽  
Hölder's Inequality

We present a new reversed version of a generalized sharp Hölder's inequality which is due to Wu and then give a new refinement of Hölder's inequality. Moreover, the obtained result is used to improve the well-known Popoviciu-Vasić inequality. Finally, we establish the time scales version of Beckenbach-type inequality.

scholarly journals Some new dynamic inequalities with several functions of Hardy type on time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adnane Hamiaz ◽  
Waleed Abuelela ◽  
Samir H. Saker ◽  
Dumitru Baleanu
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Chain Rule ◽  
Integration By Parts ◽  
Hölder's Inequality ◽  
Hardy Type ◽  
Do So

AbstractThe aim of this article is to prove some new dynamic inequalities of Hardy type on time scales with several functions. Our results contain some results proved in the literature, which are deduced as limited cases, and also improve some obtained results by using weak conditions. In order to do so, we utilize Hölder’s inequality, the chain rule, and the formula of integration by parts on time scales.

scholarly journals Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3104
Author(s):  
Slavko Simić ◽  
Vesna Todorčević
Keyword(s):  
Generating Function ◽  
Hölder’S Inequality ◽  
Arithmetic Mean ◽  
Hölder's Inequality ◽  
Power Means ◽  
Jensen Functional ◽  
Exact Bounds ◽  
Stolarsky Means

In this article, we give sharp two-sided bounds for the generalized Jensen functional Jn(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean An(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Hölder’s inequality are obtained.

scholarly journals More on Hölder’s Inequality and It’s Reverse via the Diamond-Alpha Integral

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1716
Author(s):  
M. Zakarya ◽  
H. A. Abd El-Hamid ◽  
Ghada AlNemer ◽  
H. M. Rezk
Keyword(s):  
Linear Combination ◽  
Time Scales ◽  
Time Scale ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Special Cases ◽  
General Time

In this paper, we investigate some new generalizations and refinements for Hölder’s inequality and it’s reverse on time scales through the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. Our results as special cases extend some integral dynamic inequalities and Qi’s inequalities achieved on time scales and also include some integral disparities as particular cases when T=R.

scholarly journals Some New Dynamic Inequalities Involving Monotonic Functions on Time Scales

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
S. H. Saker ◽  
E. Awwad ◽  
A. Saied
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Chain Rule ◽  
Integration By Parts ◽  
Hölder's Inequality ◽  
Monotonic Functions ◽  
A Chain ◽  
Special Case

In this paper, we prove some new dynamic inequalities involving C- monotonic functions on time scales. The main results will be proved by employing Hölder’s inequality, integration by parts, and a chain rule on time scales. As a special case when T=R, our results contain the continuous inequalities proved by Heinig, Maligranda, Pečarić, Perić, and Persson and when T=N, the results to the best of the authors’ knowledge are essentially new.

scholarly journals Generalizations and refinements of three-tuple Diamond-Alpha integral Hölder’s inequality on time scales

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Fei Yan ◽  
Jianfeng Wang
Keyword(s):  
Time Scales ◽  
Hölder’S Inequality ◽  
Hölder's Inequality

AbstractIn this paper, based on the existing Hölder’s inequality, some new three-tuple diamond-alpha integral Hölder’s inequalities on time scales are proposed and the related theorems and corollaries are given. At the same time, we also give the relevant conclusions and proof of n-tuple diamond-alpha integral Hölder’s inequalities on time scales.

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.

Sign in / Sign up

Export Citation Format

Share Document