Quasi-convex functions and Hadamard’s inequality. (English) Zbl 0908.26015

Dragomir, S. S.; Pearce, C. E. M.

Bull. Aust. Math. Soc. 57, No. 3, 377-385 (1998).

Classical Hadamard’s inequalities \[ f\left( \frac{a+b}2 \right) \leq \frac 1{b-a}\int\limits_a^bf(x)dx\leq \frac{ f(a)+f(b)}2 \] are usually proved for convex functions on the interval \([a,b]\). In this paper, the authors prove Hadamard-type inequalities for Jensen-quasi-convex functions and for Wright-quasi-convex functions. These inequalities are substantially different from the classical ones. Extensions of the sets of functions for which one or another of the above inequalities are valid, can be found in the reviewer’s paper [Studia Univ. Babeş-Bolyai, Math. 39, No. 2, 27-32 (1994; Zbl 0868.26012)].

Reviewer: G.Toader (Cluj-Napoca)

MSC:

26D15	Inequalities for sums, series and integrals
26A51	Convexity of real functions in one variable, generalizations

Keywords:

Hadamard’s inequality; quasi-convex functions

Citations:

Zbl 0868.26012

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