中点局部K一致凸性和φ_直和

Midpoint Locally K-uniform Convexity and φ_Direct Sum

将中点局部一致凸性推广到中点局部K一致凸,并且讨论了它们之间的关系。主要研究的问题为:假定X、Y都具有中点局部一致凸性或中点局部K一致凸性,那么X pY(1<p<∞)或φ-直和XφY是否仍具有中点局部一致凸性与中点局部K一致凸性。

Midpoint locally uniform convexity is generalized to the midpoint locally K-uniform convexity, and the relation between the two cases is discussed. The following problem is discussed： suppose X, Y are either midpoint locally uniform convexity or midpoint locally K-uniform convexity, respectively, whether X＋pY （1 〈 p 〈 ∞ ） or φ- direct sum X＋φY is still either midpoint locally K-uniform convexity or midpoint locally uniform convexity.