The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable.

Udomene studied the convergence of the implicit iteration process and the explicit iteration process in a real Banach space with uniformly Ga?teaux differentiable norm and uniform normal structure, and proved that both the implicit iteration process and the explicit iteration process converge strongly to a fixed point, which is the unique solution to a variational inequality.

By the study of the relationship between generalized modulus of convexity and the coefficient of weak orthogonality,sufficient condition for Banach space X have uniform normal structure is obtained,which imply the single valued nonexpansive mapping to have fixed point,moreover which also imply the multivalued nonexpansive mapping to have fixed point.

Pointed Approach of Hutton s Uniformity;

In order to seek the topological characteristics of fuzzy implicative algebras and reveal the interior relation between logical algebras and topology,we construct a uniformity used the concept of congruence relation and collection of MP-filters which closed for finite intersection on fuzzy implicative algebras,and then induces a topology.

Milman′s modulus of smoothness and normal structure

Let X be a Banach space,and K be a nonempty bounded closed convex subset of X which has a normal structure.

In this paper, we discuss normal structure of ss( E k ), and give a criterion of midpoint local uniform convexity of ss( E k ).