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A generalization of convex functions via support properties*

Published online by Cambridge University Press:  09 April 2009

Aharon Ben-Tal  and
Adi Ben-Israel
Aharon Ben-Tal
Affiliation:
Center for Cybernetic Studies, The University of Texas, Austin, Texas 78712, U.S.A.
Adi Ben-Israel
Affiliation:
Center for Cybernetic Studies, The University of Texas, Austin, Texas 78712, U.S.A.
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Abstract

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With respect to a given family of functions F, a function is said to be F-convex, if it is supported, at each point, by some member of F. For particular choices of F one obtains the convex functions and the generalized convex functions in the sense of Beckenbach. F-convex functions are characterized and studied, retaining some essential results of classical convexity.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 3 , May 1976 , pp. 341 - 361
Copyright
Copyright © Australian Mathematical Society 1976

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