On the Generalization of Weinberger's Inequality with Alternating Signs

For given set of m positive numbers satisfying the conditions: a₁ ≥ a₂ ≥ , ... ≥ aₘ ≥ 0, the inequality ∑ₛ₌₁ᵐ (-1)ˢ⁻¹aʳₛ ≥ [ ∑ₛ₌₁ᵐ (-1)ˢ⁻¹aₛ]ʳ, r > 1, was proved by H. Weinberger. In this paper, we propose a generalized inequality with a proof. In addition, we give a counterexample to the generalization of Weinberger's result that was proposed by R. Bellman.