Related papers: A refinement of the arithmetic-geometric mean ineq…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
In this paper we consider non-commutative analogue for the arithmeticgeometric mean inequality $$a^{r}b^{1-r}+(r-1)b\geq ra$$ for two positive numbers $a,b$ and $r> 1$. We show that under some assumptions the non-commutative analogue for…
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
In this paper we give a generalization of a result of Wei.
The arithmetic mean is the mean for addition and the geometric mean is that for multiplication. Then what kind of binary operation is associated with the arithmetic-geometric mean (AGM) due to C. F. Gauss? If it is possible to construct an…
We explore the concentration properties of the ratio between the geometric mean and the arithmetic mean, showing that for certain sequences of weights one does obtain concentration, around a value that depends on the sequence.
In this paper, we show that the $\nu$-weighted arithmetic mean is greater than the product of the $\nu$-weighted geometric mean and Specht's ratio. As a corollary, we also show that the $\nu$-weighted geometric mean is greater than the…
This paper presents a brief survey of the most important and the most remarkable inequalities involving the basic arithmetic functions.
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
In this paper we shall prove a sharpened version of the Finsler-Hadwiger inequality which is a strong generalization of Weitzenbock inequality. After that we give another refinement of this inequality and in the final part we provide some…
In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean.
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
We establish an inequality of different metrics for algebraic polynomials.
As we showed in [3], a geometric inequality can be regarded as an optimization problem. In this paper we find another proof for a Chen's inequality,regarding the Ricci curvature [2] and we improve this inequality in the Lagrangian case.
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
In this paper, we sharpen and generalize Shafer-Fink's double inequality for the arc sine function.
In this article, we explore the celebrated Gr\"{u}ss inequality, where we present a new approach using the Gr\"{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr\"{u}ss-type…
The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.
In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…