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http://dx.doi.org/10.22771/nfaa.2021.26.02.13

NORMAL STRUCTURE, FIXED POINTS AND MODULUS OF n-DIMENSIONAL U-CONVEXITY IN BANACH SPACES X AND X*  

Gao, Ji (Department of Mathematics, Community College of Philadelphia)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.2, 2021 , pp. 433-442 More about this Journal
Abstract
Let X and X* be a Banach space and its dual, respectively, and let B(X) and S(X) be the unit ball and unit sphere of X, respectively. In this paper, we study the relation between Modulus of n-dimensional U-convexity in X* and normal structure in X. Some new results about fixed points of nonexpansive mapping are obtained, and some existing results are improved. Among other results, we proved: if X is a Banach space with $U^n_{X^*}(n+1)>1-{\frac{1}{n+1}}$ where n ∈ ℕ, then X has weak normal structure.
Keywords
Fixed points; modulus of n-dimensional U-convexity; normal structure; ultra-product; uniform normal structure;
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