Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 71, Issue 7-8, Pages 2771-2779Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2009.01.120
Keywords
Convex function; Jensen type inequality; Majorization; Separable tuple; Monotone tuple; Star-shaped tuple; Convex tuple
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In this paper we generalize a result of Mercer [A.McD. Mercer, A variant of Jensen's inequality, J. Inequal. Pure & Appl. Math. 4 (4) (2003) Article 73. Online: http://jipam.vu. edu.au/article.php?sid=314] on convex functions. A relationship between this result and majorization ordering is pointed out. An extension of Mercer's result to pairs of similarly separable m-tuples is given. In addition, applications are discussed for nonincreasing in mean tuples, star-shaped tuples and convex tuples. (C) 2009 Elsevier Ltd. All rights reserved.
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