O-Convexity of Orlicz-Bochner Spaces with Orlicz Norm

Abstract

In this paper we give some characterizations of O-convexity of Banach spaces, and show the criteria for O-convexity in Orlicz-Bochner function space $L_M(\mu,\,X)$ and Orlicz-Bochner sequence space $l_M(X_s)$ endowed with Orlicz norm. Moreover, we give a sufficient condition for the dual of such a space to have the fixed point property.