tailieunhanh - Báo cáo hóa học: " Research Article Abstract Convexity and Hermite-Hadamard Type Inequalities"

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 Abstract Convexity and Hermite-Hadamard Type Inequalities | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 943534 13 pages doi 2009 943534 Research Article Abstract Convexity and Hermite-Hadamard Type Inequalities Gabil R. Adilov1 and Serap Kemali2 1 Department of Primary Education Faculty of Education Mersin University 33169 Mersin Turkey 2 Vocational School of Technical Sciences Akdeniz University 07058 Antalya Turkey Correspondence should be addressed to Serap Kemali skemali@ Received 24 February 2009 Accepted 8 May 2009 Recommended by Kunquan Lan The deriving Hermite-Hadamard type inequalities for certain classes of abstract convex functions are considered totally the inequalities derived for some of these classes before are summarized new inequalities for others are obtained and for one class of these functions the results on R2 are generalized to R . By considering a concrete area in Rf the derived inequalities are illustrated. Copyright 2009 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 Studying Hermite-Hadamard type inequalities for some function classes has been very important in recent years. These inequalities which are well known for convex functions have been also found in different function classes see 1-5 . Abstract convex function is one of this type of function classes. Hermite-Hadamard type inequalities are studied for some important classes of abstract convex functions and the concrete results are found 6-9 . For example increasing convex-along-rays ICAR functions which are defined in R2_ are considered in 8 . First a correct inequality for these functions is given. For each x0 y0 e R2. 0 there exists a number b xo yo 0 such that Kx0 y0 min x y - 1 x0 y0 f x y - f xo y0 for all x y . Then based on previous inequality the .