Abstract
A recent refinement of the classical discrete Jensen inequality is given by Horvath and Pecaric. In this paper, the corresponding weighted mixed symmetric means and Cauchy-type means are defined. We investigate the exponential convexity of some functions, study mean value theorems, and prove the monotonicity of the introduced means.
Highlights
Introduction and Preliminary ResultsA new refinement of the discrete Jensen inequality is given in 1
We investigate the exponential convexity of some functions, study mean value theorems, and prove the monotonicity of the introduced means
For γ, η ∈ R and k ≥ l ≥ 1, we introduce the mixed symmetric means with positive weights related to 1.37 as follows: Mη2,γ Il :
Summary
Introduction and Preliminary ResultsA new refinement of the discrete Jensen inequality is given in 1. Η ∈ R, we introduce the mixed symmetric means with positive weights as follows: Mη1,γ Ik, k : . l il tIk ,l i1,...,il ∈Il il l pis s 1 αIk,is h ◦ g−1
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