Related papers: On a mixed arithmetic-geometric mean inequality
In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite-Hadamard integral inequality for mappings whose derivatives are $s$-$(\alpha,m)$-convex.The generalised integral…
We prove a multivariate version of Hoeffding's inequality about the distribution of homogeneous polynomials of Rademacher functions. The proof is based on such an estimate about the moments of homogeneous polynomials of Rademacher functions…
We prove Gagliardo-Nirenberg inequalities on some classes of manifolds, Lie groups and graphs.
Let $\mathcal{A}$ be a unital $JB$-algebra and $A,~B\in\mathcal{A}$, we extend the weighted geometric mean $A\sharp_r B$, from $r\in [0,1]$ to $r\in (-1, 0)\cup(1, 2)$. We will notice that many results will be reversed when the domain of…
The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different…
In this paper we present some inequalities involving operator decreasing functions and operator means. These inequalities provide some reverses of operator Acz\'el inequality dealing with the weighted geometric mean.
We find an integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace and cosine Fourier transforms. Using positivity conditions for the weight in this…
We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
In this paper our aim is to present some Landen inequalities for Gaussian hypergeometric functions, confluent hypergeometric functions, generalized Bessel functions and for general power series. Our main results complement and generalize…
In this paper, we obtain some new upper bounds for differantiable mappings whose q-th powers are geometrically convex and monotonically decreasing by using the H\"older inequality, Power mean inequality and properties of modulus.
In this paper, we establish Hermite-Hadamard inequality for interval-valued convex function on the co-ordinates on the rectangle from the plane. We also present Hermite-Hadamard inequality for the product of interval-valued convex functions…
We obtain simple proofs of certain inequalites for bivariate means.
We collect some results in combinatorial geometry that follow from an inequality of Langer in algebraic geometry. Langer's inequality gives a lower bound on the number of incidences between a point set and its spanned lines, and was…
We prove Ehrhard's inequality using interpolation along the Ornstein-Uhlenbeck semi-group. We also provide an improved Jensen inequality for Gaussian variables that might be of independent interest.
In this paper, we generalise an interesting geometry problem from the 1995 edition of the International Mathematical Olympiad (IMO) using analytic geometry tools.
We previously extended the Marsden-Ratiu reduction theorem in Poisson geometry by means of graded geometry (see Part I of Arxiv:1009.0948) . In this note we provide the background material about graded geometry necessary for the proof.…
In this paper, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind.
Let $(M,d)$ be a separable and complete geodesic space with curvature lower bounded, by $\kappa\in \mathbb R$, in the sense of Alexandrov. Let $\mu$ be a Borel probability measure on $M$, such that $\mu\in\mathcal P_2(M)$, and that has at…
A positive real interval, [a, b], can be partitioned into sub-intervals such that sub-interval widths divided by sub-interval "average" values remains constant. That both Arithmetic Mean and Geometric Mean "average" values produce constant…