Some inequalities of Hermite-Hadamard type for s-convex functions

Alomari, Mohammad W.; Darus, Maslina; Kirmaci, Uˇgur S.

doi:10.1016/s0252-9602(11)60350-0

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Introduction3

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Theorem 12 ([3]1

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2012

2023

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Cited by 66 publications

(53 citation statements)

References 14 publications

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“…To prove our main results, we use following Lemma which was used by Alomari et al (see [1]). Lemma 1.…”

Section: Resultsmentioning

confidence: 99%

New Hadamard-type inequalities for functions whose derivatives are $(\alpha ,m)-$convex functions

2014

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In this paper some new inequalities are proved related to left hand side of Hermite-Hadamard inequality for the classes of functions whose derivatives of absolute values are (α, m)−convex. IntruductionThe classical Hermite-Hadamard inequality gives us an estimate of the mean value of a convex function f : I ⊆ R → R which is well-known in the literature as following;The concept of m−convexity has been introduced by Toader in [5], as following:for all x, y ∈ [0, b] and t ∈ [0, 1] . We say that f is m−concave if −f is m−convex. In [12], Miheşan gave definition of (α, m)−convexity as following;Denote by K

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“…To prove our main results, we use following Lemma which was used by Alomari et al (see [1]). Lemma 1.…”

Section: Resultsmentioning

confidence: 99%

New Hadamard-type inequalities for functions whose derivatives are $(\alpha ,m)-$convex functions

2014

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“…In [2], the authors obtained the estimate of the left-hand side of Hermite-Hadamard's inequality for s-convex functions. …”

Section: Theorem 12 ([3]mentioning

confidence: 99%

Hermite-Hadamard type inequalities for operator s-preinvex functions

Wang¹,

Liu²

2015

J. Nonlinear Sci. Appl.

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“…With the improvement of the concept of convexity, such as s-convex, (α, m)-convex, (α, m)-preinvex and so on, some new results for Hermite-Hadamard's inequality were obtained. For more recent results, one can see [2,3,5,8,[11][12][13]15] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%