tailieunhanh - Báo cáo hóa học: " Research Article Hermite-Hadamard-Type Inequalities for Increasing Positively Homogeneous Functions"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Hermite-Hadamard-Type Inequalities for Increasing Positively Homogeneous Functions | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 21430 10 pages doi 2007 21430 Research Article Hermite-Hadamard-Type Inequalities for Increasing Positively Homogeneous Functions G. R. Adilov and S. Kemali Received 20 October 2006 Accepted 6 June 2007 Recommended by Kok Lay Teo We study Hermite-Hadamard-type inequalities for increasing positively homogeneous functions. Some examples of such inequalities for functions defined on special domains are given. Copyright 2007 G. R. Adilov and S. Kemali. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Recently Hermite-Hadamard-type inequalities and their applications have attracted considerable interest as shown in the book 1 for example. These inequalities have been studied for various classes of functions such as convex functions 1 quasiconvex functions 2-4 p-functions 3 5 Godnova-Levin type functions 5 r-convex functions 6 increasing convex-along-rays functions 7 and increasing radiant functions 8 and it is shown that these inequalities are sharp. For instance if f 0 1 R is an arbitrary nonnegative quasiconvex function then for any u e 0 1 one has see 3 11 . f u f x dx min u 1 - u 0 and the inequality is sharp. In this paper we consider one generalization of Hermite-Hadamard-type inequalities for the class of increasing positively homogeneous of degree one functions defined on R x e Rn Xi 0 i 1 2 3 . n . The structure of the paper is as follows in Section 2 certain concepts of abstract convexity definition of increasing positively homogeneous of degree one functions and its important properties are given. In Section 3 Hermite-Hadamard-type inequalities for 2 Journal of Inequalities and Applications the class of increasing positively homogeneous of degree one functions are considered.