Abstract

In recent years some papers have appeared containing generalizations of the concept of convexity with the help of the notion of measure of noncompactness. Furthermore, some authors have introduced the concept of near uniform convexity by means of the Hausdorff measure and of weak near uniform convexity by means of the De Blasi measure. In this work we present a generalization of these concepts by means of a general set quantity.

Keywords: The Hausdorff and the De Blasi measures, nearly and locally nearly uniformly convex space, set quantity, reflexive Banach space.

MSC: 46A25, 46B10

Pages:  71--78     

Volume  52 ,  Issue  3$-$4 ,  2000