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

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)].


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


Zbl 0868.26012
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[1] Dragomir, Soochow J. Math. 21 pp 335– (1995)
[2] Dragomir, Anal. Num. Théor. Approx. 19 pp 29– (1990)
[3] Dragomir, Mat. Balkanica 6 pp 215– (1992)
[4] DOI: 10.1016/0022-247X(92)90233-4 · Zbl 0758.26014
[5] DOI: 10.2307/2307675 · Zbl 0057.04801
[6] DOI: 10.1007/BF01457624 · JFM 36.0446.04
[7] DOI: 10.2307/2306432 · Zbl 0072.05302
[8] DOI: 10.1137/1009007 · Zbl 0164.06501
[9] DOI: 10.2307/2306433 · Zbl 0072.05303
[10] Hewitt, Real and abstract analysis (1965)
[11] Hardy, Inequalities (1934)
[12] Roberts, Convex functions (1973)
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