Means for Divided Differences and Exponential Convexity

In this paper we obtain two means for divide differences using two majorization type results where one is related with Schur convexity. We examine their monotonicity property using exponentially convex functions.

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Published inMediterranean journal of mathematics Vol. 9; no. 1; pp. 187 - 198
Main Authors Pavić, Zlatko, Pečarić, Josip, Vukelić, Ana
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.02.2012
Subjects
Mathematics
Mathematics and Statistics
exponentially convex function
Divided differences
26D20
Schur means
Stolarsky means
convex function
26D99
log-convexity
majorization
Schur convex function
26D15
continuous extensions
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Abstract In this paper we obtain two means for divide differences using two majorization type results where one is related with Schur convexity. We examine their monotonicity property using exponentially convex functions.
AbstractList In this paper we obtain two means for divide differences using two majorization type results where one is related with Schur convexity. We examine their monotonicity property using exponentially convex functions.
Author Pavić, Zlatko
Pečarić, Josip
Vukelić, Ana
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Issue 1
Keywords exponentially convex function
Divided differences
26D20
Schur means
Stolarsky means
convex function
26D99
log-convexity
majorization
Schur convex function
26D15
continuous extensions
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References J. Jakšetić, J. Pečarić, 4-points Stolarsky Means, to appear in Mediterranean Journal of Mathematics
BernsteinS.N.Sur les fonctions absolument monotonesActa Math.19295216610.1007/BF02592679
MarshallA.W.I. Olkin, Inequalities: Theory of Majorization and Its Applications1979New YorkAcademic Press
D. S. Mitrinović, J. E. Pečarić, On Some Inequalities for Monotone Functions, Boll. Unione. Mat. Ital. (7) 5-13, 407-416, 1991.
X. Aimin, C. Zhongdi, An inequality for divided differences in high dimensions, J. Inequal. Pure Appl. Math. 10(4) (2009), Article 103, 6p.
D. S. Mitrinović, J. Pečarić and A. M. Fink, Classical and new inequalities in analysis, Kluwer Academic Publishers, The Netherlands, 1993.
AkhiezerN.I.The Classical Moment Problem and Some Related Questions in Analysis1965EdinburghOliver and Boyd0135.33803
A. I. Kechriniotis, N. D. Assimakis, On the inequlity of the difference of two integral means and applications for pdfs, JIPAM 8(1) (2007), Art. 10, 6p.
J. E. Pečarić, F. Proschan and Y. L. Tong, Convex functions, partial orderings, and statistical applications, Mathematics in science and engineering, vol. 187 Academic Press, 1992.
AndrewsG.The Theory of Partitions, Encyclopedia Math. Appl. 121976ReadingAddison-Wesley
MacmahonP.A.Combinatory Analysis, I, II1960New YorkChelsea
J. Pečarić, M. Rodić Lipanović, On an inequality for divided differences, Asian-European Journal of MAthematics 1(1) (2008), 113-120.
AtkinsonK.E.An Introduction to Numerical Analysis19892New YorkWiley0718.65001
PečarićJ.EZwickD.n-Convexity and MajorizationRocky Mountain J. Math19891930331110161830692.2600510.1216/RMJ-1989-19-1-303
A. de Morgan, The Differential and Integral Calculus (Chapter XVIII, On Interpolation and Summation, page 550), Baldwin and Cradock, London, 1842.
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References_xml – reference: D. S. Mitrinović, J. E. Pečarić, On Some Inequalities for Monotone Functions, Boll. Unione. Mat. Ital. (7) 5-13, 407-416, 1991.
– reference: J. E. Pečarić, F. Proschan and Y. L. Tong, Convex functions, partial orderings, and statistical applications, Mathematics in science and engineering, vol. 187 Academic Press, 1992.
– reference: J. Pečarić, M. Rodić Lipanović, On an inequality for divided differences, Asian-European Journal of MAthematics 1(1) (2008), 113-120.
– reference: A. I. Kechriniotis, N. D. Assimakis, On the inequlity of the difference of two integral means and applications for pdfs, JIPAM 8(1) (2007), Art. 10, 6p.
– reference: BernsteinS.N.Sur les fonctions absolument monotonesActa Math.19295216610.1007/BF02592679
– reference: AndrewsG.The Theory of Partitions, Encyclopedia Math. Appl. 121976ReadingAddison-Wesley
– reference: X. Aimin, C. Zhongdi, An inequality for divided differences in high dimensions, J. Inequal. Pure Appl. Math. 10(4) (2009), Article 103, 6p.
– reference: J. Jakšetić, J. Pečarić, 4-points Stolarsky Means, to appear in Mediterranean Journal of Mathematics
– reference: AkhiezerN.I.The Classical Moment Problem and Some Related Questions in Analysis1965EdinburghOliver and Boyd0135.33803
– reference: MacmahonP.A.Combinatory Analysis, I, II1960New YorkChelsea
– reference: AtkinsonK.E.An Introduction to Numerical Analysis19892New YorkWiley0718.65001
– reference: PečarićJ.EZwickD.n-Convexity and MajorizationRocky Mountain J. Math19891930331110161830692.2600510.1216/RMJ-1989-19-1-303
– reference: D. S. Mitrinović, J. Pečarić and A. M. Fink, Classical and new inequalities in analysis, Kluwer Academic Publishers, The Netherlands, 1993.
– reference: MarshallA.W.I. Olkin, Inequalities: Theory of Majorization and Its Applications1979New YorkAcademic Press
– reference: A. de Morgan, The Differential and Integral Calculus (Chapter XVIII, On Interpolation and Summation, page 550), Baldwin and Cradock, London, 1842.
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Mathematics and Statistics
Title Means for Divided Differences and Exponential Convexity
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