Abstract
In this paper, the famous Copson inequality has been improved. We obtain some new results by a different method.
Highlights
Suppose that ak >, p >, we obtain the following Hardy inequality: p p– p∞ ∞ apn > n= n p n ak . k= ( . )Hardy’s inequality plays an important role in the field of analysis; see [ – ]
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Competing interests The author declares that they have no competing interests
Summary
Suppose that ak > , p > , we obtain the following Hardy inequality:. n p n ak. Suppose that ak > , p > , we obtain the following Hardy inequality:. Some generalizations and strengthening of Hardy’s inequality have been obtained in [ – ]. Definition [ ] Let G ⊆ Rn be a convex set, φ : H → R be a continuous function. If φ αx + ( – α)y ≤ (≥)αφ(x) + ( – α)φ(y) holds for all x, y ∈ G, α ∈ [ , ], the function φ is convex (concave). Lemma (Hermite-Hadamard’s inequality) Let φ : [a, b] → R be a convex (concave) function.
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