Some new results on the Fejér and Hermite-Hadamard inequalities

Huy, Vu Nhat; Ngô, Quô ́c-Anh

doi:10.1216/rmj-2013-43-5-1625

Cited by 24 publications

(27 citation statements)

References 4 publications

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“…A function: I ⊆ R → R is said to belong to the class of MT(I), if it is nonnegative and for all x, y ∈ I and t ∈ (0, 1) satisfies the following inequality: For other recent results concerning Hermite-Hadamard type inequalities through various classes of convex functions, see [1,3,5,7,8,9,12,10,17,20,22,24,25,28] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals

Liu¹,

Wen²,

Park³

2016

J. Nonlinear Sci. Appl.

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Section: Introductionmentioning

confidence: 99%

Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals

Liu¹,

Wen²,

Park³

2016

J. Nonlinear Sci. Appl.

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“…Hadamard's inequality for convex functions has received renewed attention in recent years and a remarkable variety of refinements and generalizations have been found in [1,2,3,4,6,7,8,11,12,15,16] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Hermite-Hadamard-like type inequalities for twice differentiable MT-convex functions

Park¹

2015

ams

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In this paper, we establish some new Hermite-Hadamard-like type inequalities for continuously twice differentiable (α, m)-geometric-arithmetically convex functions. Mathematics Subject Classification: 26A51, 26D15Keywords: Hermite-Hadamard-type inequality, Hölder's inequality, Pólya inequality, (α, m)-GA-convexityare respectively called the weighted geometric mean of two positive numbers x and y and the weighted arithmetic mean of f (x) and f (y). Recently, in [5, 8], Ji et al. introduced the concepts of (α, m)-geometricarithmetically convex function as follows: Definition 2. The function f : [0, b] → R is said to be (α, m)-geometricarithmetically convex, or simply speaking, (α, m)-GA-convex, where (α, m) ∈ [0, 1] 2 , if the inequality f (x t y m(1−t) ) ≤ t α f (x) + m(1 − t α )f (y) holds, for all x, y ∈ [0, b] and t ∈ [0, 1]. Then, also Ji et al.[5] obtained the Hermite-Hadamard type inequalities for (α, m)-GA-convex function as follows: Theorem 1.1. Let f : R 0 = [0, ∞) → R be a differentiable function and f ∈ L([a, b]) for 0 < a < b < ∞. If |f | q is an (α, m)-geometric-arithmetically convex function on [0, max{a

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“…Hermite-Hadamard's inequalities for convex functions, (α, m)-convex functions, and s-convex functions in the second sense have received renewed attention in recent years and a remarkable variety of refinements and generalizations have been found in [1] and [5]- [11] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Generalized Hermite-Hadamard-like type inequalities for differentiable harmonically quasi-convex functions

Park¹

2014

ams

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Some new results on the Fejér and Hermite-Hadamard inequalities

Cited by 24 publications

References 4 publications

Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals

Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals

Hermite-Hadamard-like type inequalities for twice differentiable MT-convex functions

Generalized Hermite-Hadamard-like type inequalities for differentiable harmonically quasi-convex functions

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