Well Behaved Asymptotical Convex Functions

J.P. Crouzeix; A.A. Auslender

doi:10.1016/s0294-1449(17)30017-3

JournalsaihpcVol. 6pp. 101–121

Well Behaved Asymptotical Convex Functions

J.P. Crouzeix
Département de Mathématiques Appliquées, Université Blaise Pascal, B.P.45, 63170 Aubière, France
A.A. Auslender
Département de Mathématiques Appliquées, Université Blaise Pascal, B.P.45, 63170 Aubière, France

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Abstract

In this paper, we introduce the class $F$ of proper closed convex functions for which satisfy the following property.

“For all sequences ${x_{n}}$ , ${c_{n}}$ such that $c_{n} \in \partial f (x_{n})$ and $n \to \infty lim c_{n} = 0$ we have $n \to \infty lim f (x_{n}) = in f (f (x) ∣ x \in R^{N})$ ”

Characterizations and applications are then given.

Cite this article

J.P. Crouzeix, A.A. Auslender, Well Behaved Asymptotical Convex Functions. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), pp. 101–121

DOI 10.1016/S0294-1449(17)30017-3