Liangcheng Wang, Lihong Liu, Xiu-Fen Ma
Abstract
Let X be a real linear space and I ⊆ X be a non-empty convex set. f: I → R is called a convex function, if for every x, y ∈ I and any t ∈ (0, 1), we have (see [1]) f(tx + (1 − t)y) ≤ tf(x) + (1 − t)f(y). Let f be a convex function on I. For a given positive integer n> 2 and any xi ∈ I (i =
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Let X be a real linear space and I ⊆ X be a non-empty convex set. f: I → R is called a convex function, if for every x, y ∈ I and any t ∈ (0, 1), we have (see [1]) f(tx + (1 − t)y) ≤ tf(x) + (1 − t)f(y). Let f be a convex function on I. For a given positive integer n> 2 and any xi ∈ I (i =
Key concepts: Jensen's inequality, Mathematics, Convex function, Inequality, Kantorovich inequality, Ky Fan inequality, Log sum inequality, Inequality of arithmetic and geometric means