scholarly journals Some new generalizations of Hardy's integral inequality

2006 ◽  
Vol 2006 ◽  
pp. 1-15
Author(s):  
S. K. Sunanda ◽  
C. Nahak ◽  
S. Nanda
Keyword(s):  
Integral Inequality ◽  
Hölder’S Inequality ◽  
Hölder's Inequality

We have studied some new generalizations of Hardy's integral inequality using the generalized Holder's inequality.

scholarly journals Synchronization Analysis of Multiple Integral Inequalities Driven by Steklov Operator

2021 ◽  
Vol 5 (3) ◽  
pp. 97
Author(s):  
Wedad Albalawi ◽  
Zareen A. Khan
Keyword(s):  
Integral Inequality ◽  
Hölder’S Inequality ◽  
Multiple Integral ◽  
Integral Inequalities ◽  
Integration By Parts ◽  
Hölder's Inequality ◽  
Steklov Operator

We construct a subclass of Copson’s integral inequality in this article. In order to achieve this goal, we attempt to use the Steklov operator for generalizing different inequalities of the Copson type relevant to the situations ρ>1 as well as ρ<1. We demonstrate the inequalities with the guidance of basic comparison, Holder’s inequality, and the integration by parts approach. Moreover, some new variations of Hardy’s integral inequality are also presented with the utilization of Steklov operator. We also formulate many remarks and two examples to show the novelty and authenticity of our results.

scholarly journals Generalizations of Hölder’s and Some Related Integral Inequalities on Fractal Space

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guang-Sheng Chen
Keyword(s):  
Fractional Calculus ◽  
Integral Inequality ◽  
Hölder’S Inequality ◽  
Integral Inequalities ◽  
Hölder's Inequality ◽  
Local Fractional Calculus ◽  
Related Integral ◽  
Fractal Space

Based on the local fractional calculus, we establish some new generalizations of Hölder’s inequality. By using it, some related results on the generalized integral inequality in fractal space are investigated in detail.

scholarly journals Hilbert-type inequalities for time scale nabla calculus

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
H. M. Rezk ◽  
Ghada AlNemer ◽  
H. A. Abd El-Hamid ◽  
Abdel-Haleem Abdel-Aty ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Time Scale ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Arbitrary Time ◽  
Hilbert Type

Abstract This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, Hölder’s inequality, and Jensen’s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.

scholarly journals Extensions and Applications of Power-Type Aczél-Vasić-Pečarić’s Inequalities

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Kun Chen ◽  
Fei Yan ◽  
Hong-Ying Yue
Keyword(s):  
Hölder’S Inequality ◽  
Power Type ◽  
Hölder's Inequality

In this paper, we enrich and develop power-type Aczél-Vasić-Pečarić’s inequalities. First of all, we give some new versions of theorems and corollaries about Aczél-Vasić-Pečarić’s inequalities by quoting some lemmas. Moreover, in combination with Hölder’s inequality, we give some applications of the new version of Aczél-Vasić-Pečarić’s inequality and give its proof process.

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