Antoine and Zouaki ([1] and [16]) have given the existence of a continuous selection of (1.1) in the particular case where M − x0 and N − y0 are closed convex cones . In this paper, we extend this result when M (resp. N) approximates continuously its Clarke tangent cone at x0 (resp. y0) (see Definition 2.2). This property is verified at x0 for an important class of sets. We get among others: se...

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

We construct a Kähler structure (which we call a generalised Kähler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a 1-parameter family of compatible Sasaki structures. We determine those generalised Kähler cones which are Bochner-flat and we study their local geometry. We prove that any Bochner-flat Kähler manifold of complex dimension bigger than two ...

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.

We show that a locally Lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point. We present a sufficient condition for the semismoothness of solutions to generalized equations over cone reducible (nonpolyhedral) convex sets. We prove that the semismoothness of solutions to the Moreau-Yosida regularization of a lower sem...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

 The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy n-normed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy n-normed spaces. Also we givesome remarks in locally convex topology generate...

In the setup of i.i.d. observations and a real valued differentiable functional T , locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of T ) and for the confidence probability of lower confidence limits (for the value of T ), in the case that the tangent set is only a convex cone. The bounds, and the tests and estimators which achieve the ...

Given a closed convex cone P with nonempty interior in a locally convex vector space, and a set A ⊂ Y , we provide various equivalences to the implication A ∩ (−int P ) = ∅ =⇒ co(A) ∩ (−int P ) = ∅, among them, to the pointedness of cone(A + int P ). This allows us to establish an optimal alternative theorem, suitable for vector optimization problems. In addition, we characterize the two-dimens...