A generalization of the arithmetic-geometric means inequality

A Refinement of the Inequality between Arithmetic and Geometric Means

In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement. (1) exp 2 1 − n i=1 α i x

An Inequality between Compositions of Weighted Arithmetic and Geometric Means

Let P denote the collection of positive sequences defined on N. Fix w ∈ P. Let s, t, respectively, be the sequences of partial sums of the infinite series ∑ wk and ∑ sk, respectively. Given x ∈ P, define the sequences A(x) and G(x) of weighted arithmetic and geometric means of x by An(x) = n ∑ k=1 wk sn xk, Gn(x) = n ∏ k=1 x wk/sn k , n = 1, 2, . . . Under the assumption that log t is concave, ...

The matrix arithmetic-geometric mean inequality revisited

An Optimal Double Inequality among the One-Parameter, Arithmetic and Geometric Means

In the present paper, we answer the question: for 0 1    fixed, what are the greatest value   p  and the least value   q  such that the double inequality           , , 1 , p q , J a b A a b G a b J a b       holds for all with ? where for , the one-parameter mean , 0 a b  a b  p R    , p J a b  , , arithmetic mean  A a b     and geometric mean of two positive...

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...