(alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type
(alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type
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.
Keywords:
Convex function, m-Convex function, (alpha;m)-Convex function, (alpha;m1;m2)-Convex function Hermite-Hadamard type inequality,
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- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi