Implications between approximate convexity properties and approximate Hermite-Hadamard inequalities
نویسندگان
چکیده
منابع مشابه
On Approximate Hermite–hadamard Type Inequalities
The main results of this paper offer sufficient conditions in order that an approximate lower Hermite–Hadamard type inequality implies an approximate Jensen convexity property. The key for the proof of the main result is a Korovkin type theorem.
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In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...
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Keywords: m-convex functions Hermite–Hadamard inequalities Hölder inequality Power-mean inequality a b s t r a c t In this paper we give some estimates to the right-hand side of Hermite–Hadamard inequality for functions whose absolute values of second derivatives raised to positive real powers are m-convex.
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It is shown that a locally Lipschitz function is approximately convex if, and only if, its Clarke subdifferential is a submonotone operator. Consequently, in finite dimensions, the class of locally Lipschitz approximately convex functions coincides with the class of lower-C functions. Directional approximate convexity is introduced and shown to be a natural extension of the class of lower-C fun...
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ژورنال
عنوان ژورنال: Central European Journal of Mathematics
سال: 2012
ISSN: 1895-1074,1644-3616
DOI: 10.2478/s11533-012-0027-5