In this note, we investigate the generalized modulus of convexity δ(λ) and the generalized modulus smoothness p(λ). We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coeffici...In this note, we investigate the generalized modulus of convexity δ(λ) and the generalized modulus smoothness p(λ). We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coefficient of a KSthe sequence space X and δX(λ). We show that, for a wide class of class the sequence spaces X, if for some ε∈(0, 9/10] holds δx(e) 〉 1/3(1- √3/2)ε, then X has normal structure.展开更多
Let X be a Banach space with a weak uniform normal structure and C a non–empty convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t ∈...Let X be a Banach space with a weak uniform normal structure and C a non–empty convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t ∈? S} of selfmappings on C satisfying展开更多
基金supported by National Fund for Scientific Research of the Bulgarian Ministry of Education and Science, Contract MM-1401/04
文摘In this note, we investigate the generalized modulus of convexity δ(λ) and the generalized modulus smoothness p(λ). We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coefficient of a KSthe sequence space X and δX(λ). We show that, for a wide class of class the sequence spaces X, if for some ε∈(0, 9/10] holds δx(e) 〉 1/3(1- √3/2)ε, then X has normal structure.
基金supported both by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,P.R.C.by the National Natural Science Foundation 19801023
文摘Let X be a Banach space with a weak uniform normal structure and C a non–empty convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t ∈? S} of selfmappings on C satisfying