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A new class of Banach space with the drop property

Published online by Cambridge University Press:  30 January 2012

Suyalatu Wulede  and
Wudunqiqige Ha
Suyalatu Wulede
Affiliation:
College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, People's Republic of China ([email protected])
Wudunqiqige Ha
Affiliation:
Basic Department, Inner Mongolia Trade College, Huhhot 010010, People's Republic of China ([email protected])
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Abstract

We discuss a new class of Banach spaces which are wider than the strongly convex spaces introduced by Congxin Wu and Yongjin Li. We prove that the new class of Banach spaces lies strictly between either the class of uniformly convex spaces and strongly convex spaces or the class of fully k-convex spaces and strongly convex spaces. The new class of Banach spaces has inclusive relations with neither the class of locally uniformly convex spaces nor the class of nearly uniformly convex spaces. We obtain in addition some characterizations of this new class of Banach spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 1 , February 2012 , pp. 215 - 224
Copyright
Copyright © Royal Society of Edinburgh 2012

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