%A SONG Zhen-yun, HU Fu-gao
%T *A**M*(*s*)-Convex function and its Jensen-type inequality
%0 Journal Article
%D 2018
%J Journal of East China Normal University(Natural Science)
%R 10.3969/j.issn.1000-5641.2018.03.006
%P 46-54,120
%V 2018
%N 3
%U {https://xblk.ecnu.edu.cn/CN/abstract/article_25506.shtml}
%8 2018-05-25
%X Based on the convexity and general convexity of a function, the authors study extending issues of a convex function. Firstly, the concept and sign of weighted *r*-th power *s*-mean of *n* positives are introduced; secondly, the *A**M*(*s*)-convex function is defined by weighted *r*-th power *s*-mean; thirdly, the judgment theorem and operation properties of *A**M*(*s*)-convex function are discussed; and finally, the Jensen-type inequality of the *A**M*(*s*)-convex function is proved and an equivalent form is provided. The study shows that the *A**M*(*s*)-convex function is a subset of general convex functions that includes many convex functions. Studying the *A**M*(*s*)-convex function with the method of weighted *r*-th power *s*-mean is an effective way of extending and studying convex functions. This method explores a new approach to extending and studying convex functions.