in this paper, we first present a new important property for bouligand tangent cone (contingent cone) of a star-shaped set. we then establish optimality conditions for pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

This paper deals with a property which is equivalent to generalised-lushness for separable spaces. It thus may be seemed as geometrical of Banach space ensures the have Mazur–Ulam property. We prove that X enjoys this if and only C(K, X) also show same result holds $$L_\infty (\mu ,X)$$ $$L_1(\mu .

Using a technique due to Jiménez–Rodríguez, first we prove the complete latticeability of set disjoint non-norm null weakly sequences and regular-polynomially in Banach lattices. Then apply mother vector ? ? ( E ) ? s $\lambda _\pi (E) \setminus \lambda _s(E)$ , which implies ? p ? ? | $(\ell _p\widehat{\otimes }_{|\pi |}E)\setminus (\ell }_{\pi }E)$ where is lattice 1 < ? $1 \infty$ .

X iv :m at h/ 04 06 10 8v 1 [ m at h. FA ] 6 J un 2 00 4 QUADRATIC REVERSES OF THE CONTINUOUS TRIANGLE INEQUALITY FOR BOCHNER INTEGRAL OF VECTOR-VALUED FUNCTIONS IN HILBERT SPACES SEVER S. DRAGOMIR Abstract. Some quadratic reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are prov...