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A Best Possible Double Inequality for Power Mean [PDF]
Journal of Applied Mathematics, 2012 We answer the question: for any p,q∈ℝ with p≠q and p≠-q, what are the greatest value λ=λ(p,q) and the least value μ=μ(p,q), such that the double inequality Mλ(a,b)
Yong-Min Li, Bo-Yong Long, Yu-Ming Chu
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Estimations of the weighted power mean by the Heron mean and related inequalities for determinants and traces [PDF]
Mathematical Inequalities & Applications, 2019 For positive real numbers a and b , the weighted power mean Pt,q(a,b) and the weighted Heron mean Kt,q(a,b) are defined as follows: For t ∈ [0,1] and q ∈ R , Pt,q(a,b) = {(1− t)aq + tbq} q and Kt,q(a,b) = (1− q)a1−tbt + q{(1− t)a+ tb} .
Masatoshi Ito
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A power mean inequality for the Grötzsch ring function [PDF]
Mathematical Inequalities & Applications, 2011 The Grotzsch ring function has numerous applications in geometric function theory and its properties have been investigated by many authors. Here we extend an earlier functional inequality involving the Grotzsch ring function and the geometric mean, due to Anderson, Vamanamurthy and Vuorinen, to the case of power mean.
Gendi Wang, Xiaohui Zhang, Yu‐Ming Chu
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An optimal power mean inequality for the complete elliptic integrals
Applied Mathematics Letters, 2011 AbstractIn this work, we prove that Mp(K(r),E(r))>π/2 for all r∈(0,1) if and only if p≥−1/2, where Mp(x,y) denotes the power mean of order p of two positive numbers x and y, and K(r) and E(r) denote the complete elliptic integrals of the first and second kinds, respectively.
Miao-Kun Wang +3 more
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The sharper version for generalized power mean inequalities with negative exponent [PDF]
Journal of Mathematical Inequalities, 2023 . In this study, the generalized power mean inequalities with a negative parameter are re fi ned using an optimality theorem on the generator function. The optimality theorem requires the study of different cases for the exponents and yields a re fi nement
Ramazan Tınaztepe +6 more
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A Power Mean Inequality involving the complete elliptic integrals [PDF]
, 2013 In this paper the authors investigate a power mean inequality for a special function which is defined by the complete elliptic integrals.
Gendi Wang, Xiaohui Zhang, Yu‐Ming Chu
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Advancements in integral inequalities of Ostrowski type via modified Atangana-Baleanu fractional integral operator [PDF]
HeliyonConvexity and fractional integral operators are closely related due to their fascinating properties in the mathematical sciences. In this article, we first establish an identity for the modified Atangana-Baleanu (MAB) fractional integral operators. Using
Gauhar Rahman +4 more
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Fractional Ostrowski-type Inequalities via $(\alpha,\beta,\gamma,\delta)-$convex Function [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we are introducing for the first time a generalized class named the class of $(\alpha,\beta,\gamma,\delta)-$convex functions of mixed kind.
Ali Hassan +3 more
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Properties of the power-mean and their applications
AIMS Mathematics, 2020 Suppose $w,v>0$, $w\neq v$ and $A_{u}\left (w,v\right) $ is the $u$-order power mean (PM) of $w$ and $v$. In this paper, we completely describe the convexity of $u\mapsto A_{u}\left (w,v\right) $ on $\mathbb{R}$ and $% s\mapsto A_{u\left (s\right ...
Jing-Feng Tian +2 more
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Newton–Simpson-type inequalities via majorization
Journal of Inequalities and Applications, 2023 In this article, the main objective is construction of fractional Newton–Simpson-type inequalities with the concept of majorization. We established a new identity on estimates of definite integrals utilizing majorization and this identity will lead us to
Saad Ihsan Butt +3 more
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