- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 68 Issue: 2
- (alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type
(alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type
Authors : Huriye Kadakal
Pages : 2128-2142
Doi:10.31801/cfsuasmas.511184
View : 7 | Download : 5
Publication Date : 2019-08-01
Article Type : Research
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.Keywords : Convex function, m-Convex function, (alpha, m)-Convex function, (alpha, m1, m2)-Convex function, Hermite-Hadamard type inequality