New integral inequalities of Hermite–Hadamard type in a generalized context
Abstract:In this paper, we obtained new integral inequalities of the Hermite–Hadamard type for convex and quasi–convex functions in a generalized context.
“…For example, we can state new results on integral inequality of Hermite-Hadamard type, which can be easily proved, following the ideas of [6,7,14] inter alia.…”
In this paper, we introduce the Ω-derivative, which generalizes the classical concept of derivative. Main properties of this new derivative are revised. We also study Ω-differential equations and some of its applications.
“…For example, we can state new results on integral inequality of Hermite-Hadamard type, which can be easily proved, following the ideas of [6,7,14] inter alia.…”
In this paper, we introduce the Ω-derivative, which generalizes the classical concept of derivative. Main properties of this new derivative are revised. We also study Ω-differential equations and some of its applications.
“…For more information and to get acquainted with various extensions of Hadamard's inequality, the reader can refer to [3,5,6,7,8,9,12,14,15,16,17,19,20,21,22,23,24,25,27,35,38] and references in them.…”
In this note, starting with a lemma, we obtain several extensions of the well-known Hermite-Hadamard inequality for convex functions, using generalized weighted integral operators.
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