Results 121 to 130 of about 5,359,615 (162)

The Schur-convexity of the mean of a convex function [PDF]

open access: yesApplied Mathematics Letters, 2009
The authors establish the Schur-convexity at the upper and lower limits of the integral for the mean of a convex function. Furthermore, a new proof of the inequality \[ f\bigg(\frac{a+b}{2}\bigg)=H(0) \leq H(t) \leq H(1)= \frac1{b-a}\int^ b_ a f(x)\,dx \] obtained by \textit{S. S. Dragomir} [J. Math. Anal. Appl. 167, No. 1, 49--56 (1992; Zbl 0758.26014)
Huan-nan Shi
exaly   +4 more sources

Characterization of Inner Product Spaces by Strongly Schur-Convex Functions [PDF]

open access: yesResults in Mathematics, 2020
AbstractInvolving the notion of strongly Schur-convex functions we give a new characterization of inner product spaces among norm spaces. We also present a representation theorem for functions which generate strongly Schur-convex sums.
Mirosław Adamek
exaly   +2 more sources
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Schur convexity for some differences of convex functions

Rocky Mountain Journal of Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Safaei, Nozar, Barani, Ali
exaly   +3 more sources

Schur-Convex Functions

2010
For any given partial ordering \(\preceq\)of a setX, real-valued functionsf1 defined onXwhich satisfyf(x)= f(y) wheneverx_yare var- 2 iously referred to as “monotonic,” “isotonic,” or “order-preserving.” 3 For the ordering of majorization, the order-preserving functions were 4 first systematically studied by I. Schur (1923).
Albert W. Marshall   +2 more
openaire   +1 more source

SCHUR CONVEX FUNCTIONALS: FATOU PROPERTY AND REPRESENTATION

Mathematical Finance, 2010
The Fatou property for every Schur convex lower semicontinuous (l.s.c.) functional on a general probability space is established. As a result, the existing quantile representations for Schur convex l.s.c. positively homogeneous convex functionals, established on  for either p= 1 or p=∞ and with the requirement of the Fatou property, are generalized for 
Grechuk, Bogdan, Zabarankin, Michael
openaire   +1 more source

Partition-Optimization with Schur Convex Sum Objective Functions

SIAM Journal on Discrete Mathematics, 2004
Summary: We study optimization problems over partitions of the finite set \(N = {1,\dots, n}\), where each element \(i\) in the partitioned set \(N\) is associated with a real number \(\theta^i\) and the objective associated with a partition \(\pi=(\pi_, \ldots, \pi_p)\) has the form \(F(\pi)=f(\theta_{\pi})\), where \( \theta_{\pi} = (\sum_{i\in{\pi_1}
Frank Kwang-Ming Hwang   +1 more
openaire   +3 more sources

Schur convexity for a class of symmetric functions

Science China Mathematics, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chu, Yuming, Xia, Weifeng, Zhao, Tiehong
openaire   +2 more sources

Schur-Convex Functions on $$\ell ^p$$ Spaces and Applications

Results in Mathematics, 2022
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openaire   +2 more sources

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