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We find the greatest value λ and the least value μ such that the double inequality C(λa +(1-λ)b, λb + (1-λ)a) < αA(a,b) + (1-α)T(a, b)< C(μa + (1-μ)b, μb + (1-μ)a) holds for all α (0,1) and a,… (More)
Summary: In the paper, the famous Hermite-Hadamard integral inequality for convex functionsis generalized to and reﬁned as ones for n-time differentiable functions which are s-convex in thesecond… (More)
In the paper, the authors introduce a new concept of $r$-$\varphi$-preinvex functions and establish some new integral inequalities of Hermite-Hadamard type.
The authors find the greatest value λ and the least value μ, such that the double inequality C(λa + (1-λb), λb+(1-λ)a) < αA(a, b) + (1-α)T(a,b) < C(μa + (1 - μ)b, μb + (1 - μ)a) holds for all α ∈ (0,… (More)
In this paper, a similar result of F. Qi and L. Debnath’s inequality is given, and a generalization of Alzer’s inequality is established.