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Zeitschrift für Analysis und ihre Anwendungen


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Volume 4, Issue 2, 1985, pp. 125–132
DOI: 10.4171/ZAA/142

Published online: 1985-04-30

Mean Value Theorem for Functions Possessing First Order Convex Approximations. Applications in Optimization Theory

Marcin Studniarski[1]

(1) Uniwersytet Lodzki, Poland

A mean value theorem for functions possessing first order convex approximations in the sense of Ioffe [6] is derived. It comprises two known results for convex and locally Lipschitzian functions as particular cases. This theorem is used in order to obtain a sufficient condition for a function defined on the Cartesian product of two topological vector spaces to possess a first order convex approximation. Some applications in optimization theory are also given.

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Studniarski Marcin: Mean Value Theorem for Functions Possessing First Order Convex Approximations. Applications in Optimization Theory. Z. Anal. Anwend. 4 (1985), 125-132. doi: 10.4171/ZAA/142