NORMAL STRUCTURE, FIXED POINTS AND MODULUS OF n-DIMENSIONAL U-CONVEXITY IN BANACH SPACES X AND X*
Ji Gao · Nonlinear functional analysis and applications · 2021
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_{ X*}^{ n} ( n +1) > 1 − 1/(n+1) where n ∈ N , then X has weak normal structure.