Inequalities for averages of quasiconvex and superquadratic functions
نویسندگان
چکیده
منابع مشابه
Inequalities for Averages of Convex and Superquadratic Functions
We consider the averages An(f) = 1/(n − 1) ∑n−1 r=1 f(r/n) and Bn(f) = 1/(n + 1) ∑n r=0 f(r/n). If f is convex, then An(f) increases with n and Bn(f) decreases. For the class of functions called superquadratic, a lower bound is given for the successive differences in these sequences, in the form of a convex combination of functional values, in all cases at least f(1/3n). Generalizations are for...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2016
ISSN: 1331-4343
DOI: 10.7153/mia-19-40