Results 21 to 30 of about 36,362 (173)

On matrix inequalities between the power means: Counterexamples

Linear Algebra and its Applications, 2013
We prove that the known sufficient conditions on the real parameters $(p,q)$ for which the matrix power mean inequality $((A^p+B^p)/2)^{1/p}\le((A^q+B^q)/2)^{1/q}$ holds for every pair of matrices $A,B>0$ are indeed best possible. The proof proceeds by constructing $2\times2$ counterexamples. The best possible conditions on $(p,q)$ for which $Φ(A^p)^
Audenaert, Koenraad M. R., Hiai, Fumio
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Some Bullen-Simpson type inequalities for differentiable s-convex functions [PDF]

Mathematica Moravica
Convexity is one of the fundamental principles of analysis. Over the past few decades, many important inequalities have been established for different classes of convex functions.
Meftah Badreddine, Samoudi Sara
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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, Yuming Chu
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Ostrowski's inequalities for functions whose first derivatives are s-logarithmically preinvex in the second sense [PDF]

Mathematica Moravica, 2018
In this paper, some Ostrowski's inequalities for functions whose first derivatives are s-logarithmically preinvex in the second sense are established.
Badreddine Meftah
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Some companions of Ostrowski type inequality for functions whose second derivatives are convex and concave with applications

Arab Journal of Mathematical Sciences, 2015
In this paper, we obtain some companions of Ostrowski type inequality for absolutely continuous functions whose second derivatives absolute values are convex and concave. Finally, we give some applications for special means.
M. Emin Özdemir, Merve Avci Ardic
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Some New Bullen-Type Inequalities Obtained via Fractional Integral Operators

Axioms, 2023
In this paper, we establish a new auxiliary identity of the Bullen type for twice-differentiable functions in terms of fractional integral operators.
Asfand Fahad, Saad Ihsaan Butt, Bahtiyar Bayraktar, Mehran Anwar, Yuanheng Wang   +4 more
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Fractional Hermite–Hadamard-Type Inequalities for Differentiable Preinvex Mappings and Applications to Modified Bessel and q-Digamma Functions

Mathematical and Computational Applications, 2023
The theory of convexity pertaining to fractional calculus is a well-established concept that has attracted significant attention in mathematics and various scientific disciplines for over a century.
Muhammad Tariq, Hijaz Ahmad, Asif Ali Shaikh, Sotiris K. Ntouyas, Evren Hınçal, Sania Qureshi   +5 more
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Power Mean Inequalities and Sums of Squares

Discrete & Computational Geometry
For fixed degree and increasing number of variables the dimension of the vector space of $n$-variate real symmetric homogeneous polynomials (forms) of degree $d$ stabilizes. We study the limits of the cones of symmetric nonnegative polynomials and symmetric sums of squares, when expressed in power-mean or monomial-mean basis. These limits correspond to
Jose Acevedo, Grigoriy Blekherman
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Hermite–Hadamard-type inequalities for geometrically r-convex functions in terms of Stolarsky’s mean with applications to means

Advances in Difference Equations, 2021
In 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 ...
Muhammad Amer Latif
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Some Inequalities for Power Means; a Problem from “The Logarithmic Mean Revisited” [PDF]

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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