n-CONVEXITY AND MAJORIZATION

n-CONVEXITY AND MAJORIZATION

The fact that the nth order divided difference of an (n + 2)-convex function is a symmetric, convex function of its arguments, and is therefore Schur convex, allows us to apply the theory of Majorization in order to derive inequalities for such functions. Several consequences of this result are pres...

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Veröffentlicht in:The Rocky Mountain journal of mathematics 1989, Vol.19 (1), p.303-311
Hauptverfasser: PEČARIĆ, J.E., ZWICK, D.
Format: Artikel
Sprache:eng
Schlagworte:
Convexity
Mathematical functions
Mathematical inequalities
Polynomials
Sine function
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Zusammenfassung:The fact that the nth order divided difference of an (n + 2)-convex function is a symmetric, convex function of its arguments, and is therefore Schur convex, allows us to apply the theory of Majorization in order to derive inequalities for such functions. Several consequences of this result are presented. In a separate section the theory of majorization is used to compute bounds on the derivatives of polynomials.
ISSN:0035-7596
1945-3795
DOI:10.1216/RMJ-1989-19-1-303