JENSEN TYPE INEQUALITIES FOR Q-CLASS FUNCTIONS

Publisher： Cambridge University Press

E-ISSN： 1755-1633|85|1|128-142

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.85, Iss.1, 2011-10, pp. : 128-142

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Abstract

Some inequalities of Jensen type for Q-class functions are proved. More precisely, a refinement of the inequality f((1/P)∑ ni=1pixi)≤P∑ ni=1(f(xi)/pi) is given in which p1,…,pn are positive numbers, P=∑ ni=1pi and f is a Q-class function. The notion of the jointly Q-class function is introduced and some Jensen type inequalities for these functions are proved. Some Ostrowski and Hermite–Hadamard type inequalities related to Q-class functions are presented as well.

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