2000
DOI: 10.1216/rmjm/1021477248
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A Note on Schur-Convex Functions

Abstract: In this note it is proved that the integral arithmetic mean of a convex function is a Schur-convex function. Applications to Schur-convexity of logarithmic mean and gamma functions are given.

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Cited by 33 publications
(16 citation statements)
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“…Namely, for a function f : [a, b] → R such that f (4) is continuous on [a, b], the following identity is valid:…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Namely, for a function f : [a, b] → R such that f (4) is continuous on [a, b], the following identity is valid:…”
Section: Introductionmentioning
confidence: 99%
“…For example, the following theorems were given in [4,5], respectively. Also, in [6] some related results were given.…”
Section: Introductionmentioning
confidence: 99%
“…These extensions and generalizations in the theory of inequalities have made valuable contributions in many areas of mathematics. Some new generalized concepts in this point of view are quasiconvex [1], strongly convex [2], approximately convex [3], logarithmically convex [4], midconvex functions [5], pseudoconvex [6], -convex [7], -convex [8], ℎ-convex [9], delta-convex [10], Schur convex [11][12][13][14][15], and others [16][17][18][19].…”
Section: Introductionmentioning
confidence: 99%
“…The first push in that direction was made in [6], where the following theorem was proven. Throughout this paper, by I we denote a nonempty open interval in R. A decade later, a related result regarding the midpoint and trapezoid formulas was obtained in [2].…”
Section: Introductionmentioning
confidence: 99%