The Power Mean Inequality

1996 ◽  
pp. 249-254
Keyword(s):  
Power Mean ◽  
Power Mean Inequality

scholarly journals The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 380 ◽  
Author(s):  
Yongtao Li ◽  
Xian-Ming Gu ◽  
Jianxing Zhao
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Hölder Inequality ◽  
Power Mean ◽  
Weighted Arithmetic ◽  
Mathematical Equivalence ◽  
Power Mean Inequality ◽  
Mathematical Relations

In the current note, we investigate the mathematical relations among the weighted arithmetic mean–geometric mean (AM–GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM–GM inequality, the weighted power-mean inequality and the Hölder inequality are fully achieved. The new results are more generalized than those of previous studies.

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 An optimal power mean inequality for the complete elliptic integrals

2011 ◽  
Vol 24 (6) ◽  
pp. 887-890 ◽  
Author(s):  
Miao-Kun Wang ◽  
Yu-Ming Chu ◽  
Ye-Fang Qiu ◽  
Song-Liang Qiu
Keyword(s):  
Elliptic Integrals ◽  
Power Mean ◽  
Optimal Power ◽  
Complete Elliptic Integrals ◽  
Power Mean Inequality

scholarly journals Some new inequalities for convex functions via Riemann-Liouville fractional integrals

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mustafa Gürbüz ◽  
Çetin Yıldız
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Power Mean ◽  
Semigroup Property ◽  
Fractional Analysis ◽  
Power Mean Inequality ◽  
Fractional Orders ◽  
Scientific Fields ◽  
New Inequalities

AbstractFractional analysis has evolved considerably over the last decades and has become popular in many technical and scientific fields. Many integral operators which ables us to integrate from fractional orders has been generated. Each of them provides different properties such as semigroup property, singularity problems etc. In this paper, firstly, we obtained a new kernel, then some new integral inequalities which are valid for integrals of fractional orders by using Riemann-Liouville fractional integral. To do this, we used some well-known inequalities such as Hölder's inequality or power mean inequality. Our results generalize some inequalities exist in the literature.

scholarly journals Hermite–Hadamard-type inequalities for geometrically r-convex functions in terms of Stolarsky’s mean with applications to means

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Amer Latif
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Power Mean ◽  
Power Mean Inequality

AbstractIn this paper, we obtain new Hermite–Hadamard-type inequalities for r-convex and geometrically convex functions and, additionally, some new Hermite–Hadamard-type inequalities by using the Hölder–İşcan integral inequality and an improved power-mean inequality.

scholarly journals On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2153-2171 ◽  
Author(s):  
Fuat Usta ◽  
Hüseyin Budak ◽  
Mehmet Sarikaya ◽  
Erhan Set
Keyword(s):  
Fractional Integral ◽  
Type Inequality ◽  
Power Mean ◽  
Fractional Integral Operators ◽  
Convex Mappings ◽  
Special Means ◽  
Generalized Fractional Integral ◽  
Explicit Bounds ◽  
Power Mean Inequality ◽  
Generalized Fractional Integral Operators

By using contemporary theory of inequalities, this study is devoted to propose a number of refinements inequalities for the Hermite-Hadamard?s type inequality and conclude explicit bounds for the trapezoid inequalities in terms of s-convex mappings, at most second derivative through the instrument of generalized fractional integral operator and a considerable amount of results for special means. The results of this study which are the generalization of those given in earlier works are obtained for functions f where |f'| and |f''| (or |f'|q and |f''|q for q ? 1) are s-convex hold by applying the H?lder inequality and the power mean inequality.

scholarly journals Several Integral Inequalities of Hermite–Hadamard Type Related to k-Fractional Conformable Integral Operators

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1880
Author(s):  
Muhammad Tariq ◽  
Soubhagya Kumar Sahoo ◽  
Hijaz Ahmad ◽  
Thanin Sitthiwirattham ◽  
Jarunee Soontharanon
Keyword(s):  
Convex Functions ◽  
Convex Sets ◽  
Convex Geometry ◽  
Integral Operators ◽  
Symmetric Convex ◽  
Strong Correlations ◽  
Power Mean ◽  
First Order ◽  
Mathematical Sciences ◽  
Power Mean Inequality

In this paper, we present some ideas and concepts related to the k-fractional conformable integral operator for convex functions. First, we present a new integral identity correlated with the k-fractional conformable operator for the first-order derivative of a given function. Employing this new identity, the authors have proved some generalized inequalities of Hermite–Hadamard type via Hölder’s inequality and the power mean inequality. Inequalities have a strong correlation with convex and symmetric convex functions. There exist expansive properties and strong correlations between the symmetric function and various areas of convexity, including convex functions, probability theory, and convex geometry on convex sets because of their fascinating properties in the mathematical sciences. The results of this paper show that the methodology can be directly applied and is computationally easy to use and exact.

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