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Duality Inequalities and Sandwiched Functions

Borwein, Jonathan M. and Fitzpatrick, Simon (2001) Duality Inequalities and Sandwiched Functions. Nonlinear Analysis: Theory, Methods & Applications, 46 (3). pp. 365-380. ISSN 0362546X

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      Abstract

      We establish a mixed convex-Lipschitz mean value inequality from which recent results of Clarke and Ledyaev and of Lewis and Ralph follow naturally. We also provide various refinements and extensions. Finally, we answer affirmatively several open questions on the existence of ``squeeze'' theorems for a finite number of Lipschitz functions.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: nonconvex separation, sandwich theorem, mean-value inequalities, Fenchel duality, Schauder fixed point theorem, Ekeland variational principle
      Subjects: 90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming
      49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      46-xx Functional analysis > 46Nxx Miscellaneous applications of functional analysis
      26-xx Real functions > 26Bxx Functions of several variables
      47-xx Operator theory > 47Hxx Nonlinear operators and their properties
      52-xx Convex and discrete geometry > 52Axx General convexity
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 25 Nov 2003
      Last Modified: 21 Sep 2014 18:19
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/204

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