scholarly journals The Improvement of Hölder’s Inequality with r -Conjugate Exponents Relative to the L p -Norm

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xiaojun Liang ◽  
Aying Wan
Keyword(s):  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Conjugate Exponents

This paper investigates Hölder’s inequality under the condition of r -conjugate exponents in the sense that ∑ k = 1 s 1 / p k = 1 / r . Successively, we have, under r -conjugate exponents relative to the L p -norm, investigated generalized Hölder’s inequality, the interpolation of Hölder’s inequality, and generalized s -order Hölder’s inequality which is an expansion of the known Hölder’s inequality.

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 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 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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