An inequality for polymatroid functions and its applications

An inequality for polymatroid functions and its applications

An integral-valued set function f : 2 7→ Z is called polymatroid if it is submodular, non-decreasing, and f(∅) = 0. Given a polymatroid function f and an integer threshold t ≥ 1, let α = α(f, t) denote the number of maximal sets X ⊆ V satisfying f(X) < t, let β = β(f, t) be the number of minimal sets X ⊆ V for which f(X) ≥ t, and let n = |V |. We show that if β ≥ 2 then α ≤ β , where c = c(n, β...

An inequality for polymatroid functions

An integral-valued set function f : 2V 7→ Z is called polymatroid if it is submodular, non-decreasing, and f(∅) = 0. Given a polymatroid function f and an integer threshold t ≥ 1, let α = α(f, t) denote the number of maximal sets X ⊆ V satisfying f(X) < t, let β = β(f, t) be the number of minimal sets X ⊆ V for which f(X) ≥ t, and let n = |V |. We show that if β ≥ 2 then α ≤ β(log t)/c, where c...

On the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications

In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.

A companion of Ostrowski's inequality for functions of bounded variation and applications

A companion of Ostrowski's inequality for functions of bounded variation and applications are given.

An Integral Inequality and Its Applications