On an inequality of Diananda. Part III

On an Inequality of Diananda, Iii

We extend the results in part I, II on certain inequalities involving the generalized power means.

On an Inequality of Diananda - Part IV

On an inequality of Diananda. Part II

Let Pn,r(x) be the generalized weighted means: Pn,r(x) = ( ∑n i=1 qix r i ) 1/r , where Pn,0(x) denotes the limit of Pn,r(x) as r → 0+, x = (x1,x2, . . . ,xn) and qi > 0 (1 ≤ i ≤ n) are positive real numbers with ∑n i=1 qi = 1. In this paper, we let q = minqi and always assume n≥ 2, 0 ≤ x1 < x2 < ··· < xn. We defineAn(x) = Pn,1(x),Gn(x) = Pn,0(x),Hn(x) = Pn,−1(x), and we will write Pn,r for Pn,...

On an Inequality of Diananda

where Pn,0(x) denotes the limit of Pn,r (x) as r → 0+ and where qi > 0, 1≤ i≤n, are positive real numbers with ∑n i=1qi = 1 and x = (x1,x2, . . . ,xn). In this note, we let q =minqi and always assume n≥ 2 and 0≤ x1 <x2 < ···<xn. We define An(x) = Pn,1(x), Gn(x) = Pn,0(x), and Hn(x) = Pn,−1(x) and we will write Pn,r for Pn,r (x), An for An(x), and similarly for other means when there is no risk ...

Some Results on facets for linear inequality in 0-1 variables

The facet of Knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. Such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. Strong covers for facets of Knapsack ploytope has been developed in the first pa...