Results 91 to 100 of about 311,275 (193)
Note on Generalization of Power Means and Their Inequalities
Journal of Mathematical Analysis and Applications, 1999 New proofs of two results of the reviewer [J. Math. Anal. Appl. 161, No. 2, 395--404 (1991; Zbl 0753.26009)] are given.
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Some results on integral inequalities via Riemann–Liouville fractional integrals
Journal of Inequalities and Applications, 2019 In current continuation, we have incorporated the notion of s−(α,m) $s- ( {\alpha,m} ) $-convex functions and have established new integral inequalities. In order to generalize Hermite–Hadamard-type inequalities, some new integral inequalities of Hermite–
Xiaoling Li +6 more
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Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means
, 2010 We answer the question: for , what are the greatest value and the least value such that the double inequality holds for all with . Here, , , and denote the power of order , Seiffert, and geometric means of two positive numbers and , respectively.
Y. Chu, Y. Qiu, Miao-Kun Wang
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Some Inequalities for Power Means; a Problem from “The Logarithmic Mean Revisited”
The American Mathematical Monthly, 2023 We establish some inequalities comparing power means of two numbers with combinations of the arithmetic and geometric means. A conjecture from [Citation1] is confirmed.
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Exact inequalities involving power mean, arithmetic mean and identric mean
Journal of Numerical Analysis and Approximation Theory, 2011 For \(p\in \mathbb{R}\), the power mean \(M_{p}(a,b)\) of order \(p\), identric mean \(I(a,b)\) and arithmetic mean \(A(a,b)\) of two positive real numbers \(a\) and \(b\) are defined by \begin{equation*} M_{p}(a,b)= \begin{cases} \displaystyle\left(\tfrac{a^{p}+b^{p}}{2}\right)^{1/p}, & p\neq 0,\\ \sqrt{ab}, & p=0, \end{cases} \quad I(a,b ...
Yu-ming Chu, Ming-yu Shi, Yue-ping Jiang
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New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ-Convex Functions
Mathematics, 2019 In this paper, a quantum trapezium-type inequality using a new class of function, the so-called generalized ϕ -convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ϕ -convex functions is ...
Miguel J. Vivas-Cortez +3 more
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Generalization of the power means and their inequalities
Journal of Mathematical Analysis and Applications, 1991 The paper contains a generalization of the power means which includes a class of positive nonlinear functionals. For these new means the author obtains generalizations of the fundamental mean inequality, Hölder's, Minkowski's and related inequalities.
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Jessen's functional, its properties and applications
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012 In this paper we consider Jessen's functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are then applied to weighted generalized power means, which yields extensions of some recent results,
Lovričević Neda +2 more
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Power means of probability measures and Ando-Hiai inequality
, 2018 Let $ $ be a probability measure of compact support on the set $\mathbb{P}_n$ of all positive definite matrices, let $t\in(0,1]$, and let $P_t( )$ be the unique positive solution of $X=\int_{\mathbb{P}_n}X\sharp_t Z d (Z)$. In this paper, we show that $$ P_t( )\leq I\quad \Longrightarrow\quad P_{\frac{t}{p}}( )\leq P_t( )$$ for every $p\geq1 ...
Kian, Mohsen, Moslehian, Mohammad Sal
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Scaled evolution of the reversed power mean inequalities
FilomatMotivated by the Hanin inequality, in this paper we study a class of reversed power mean inequalities that does not depend on a weight function. We first give the reverse of the basic power mean inequality describing the monotonic behavior of means. Then, we establish the scaled, i.e. two-parametric versions of the obtained inequalities. By scaling, we
Krnić, Mario +2 more
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