(alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type
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Date
2019-08-01
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Ankara Üniversitesi Fen Fakültesi
Abstract
In this paper, we introduce a new class of extended (alpha;m1;m2)-convex functions. Some algebraic properties of these class functions have been investigated. Some new Hermite-Hadamard type inequalities are derived. Results represent signicant refinement and improvement of the previous results. Also, the author establish a new integral identity and, by this identity, Hölder's and power mean inequality, discover some new Hermite-Hadamard type inequalities for functions whose first derivatives are (alpha;m1;m2)-convex. Our results are new and coincide with the previous results in special cases.
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Keywords
Convex function, m-Convex function, (alpha;m)-Convex function