Abstract :
In the present paper we focus on a generalization of the notion of integral convexity. This concept,
introduced in [J.Y.Wang, Y.M. Ma, The integral convexity of sets and functionals in Banach spaces, J.Math.
Anal. Appl. 295 (2004) 211–224] by replacing, in the definition of classical notion of convexity, the sum
by the integral, has interesting applications in optimal control problems. By using, instead of Bochner
integral, a more general vector integral, that of Pettis, we obtain some results on integral-extreme points of
subsets of a Banach space stronger than those given in [J.Y. Wang, Y.M. Ma, The integral convexity of sets
and functionals in Banach spaces, J. Math. Anal. Appl. 295 (2004) 211–224]. Finally, a natural example
coming from measure theory is included, in order to reflect the relationships between different kinds of
integral convexity.
© 2006 Elsevier Inc. All rights reserved.
