The generalized state space of a commutative C-algebra, denoted SH(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C-convexity is one of several non-commutative analogs of convexity which have been discussed in this context. In this paper we show that a C-extreme point of SH(C(X)) satisfies a certain spectral condition on...

This article deals with the different classes of convexity and generalizations. Firstly, we reveal the new generalization of the definition of convexity that can reduce many order of convexity. We have showed features of algebra for this new convex function. Then after we have constituted Hermite-Hadamard type inequalities for this class of functions. Finally the identity has been revealed for ...

Theorem 7.1 (Brunn-Minkowski). If A, B ⊆ R n satisfy some mild assumptions (in particular, convexity suffices), then [vol (A + B)] 1 n ≥ [vol (A)] 1 n + [vol (B)] 1 n where A + B = { a + b : a ∈ A and b ∈ B}.

In this paper, we present the notion of multimodular triangulation under a new geometrical point of view. We also show the link with multimodular functions by a new proof of the convexity theorem. This is used to de ne a partial ordering compatible with multimodularity called the cone ordering. An application in admission control in queues is then presented.

In this paper, we introduce a new class of functions which are analytic and univalent with negative coefficients defined by using a certain fractional calculus and fractional calculus integral operators. Characterization property,the results on modified Hadamard product and integrals transforms are discussed. Further, distortion theorem and radii of starlikeness and convexity are also determine...

Abstract. In this paper, we introduce a new class of functions which are analytic and univalent with negative coefficients defined by using certain fractional operators descibed in the Caputo sense. Characterization property, the results on modified Hadamard product and integral transforms are discussed. Further, distortion theorem and radii of starlikeness and convexity are also determined here.

Abstract. We introduce a new subclass corresponding to the class of k−uniformly convex and starlike functions associated with HurwitzLerch zeta functions and determine many properties like the coefficient estimates, extreme points, closure theorem, distortion bounds, radii of starlikeness and convexity. Furthermore, we obtain an integral transform results, neighborhood results, integral means i...

In this paper, a pair of multiobjective fractional variational symmetric dual problems over cones is formulated. Weak, strong and converse duality theorems are established under generalized F-convexity assumptions. Moreover, self duality theorem is also discussed. 2007 Elsevier B.V. All rights reserved.

We give several versions of local and global inverse mapping theorem for tame non necessarily smooth, mappings. Here tame mapping means a mapping which is subanalytic or, more generally, definable in some o-minimal structure. Our sufficient conditions are formulated in terms of various properties (convexity, positivity of some principal minors, contractiblity) of the space of Jacobi’s matrices ...

We provide a simpler proof of Gouweleeuw’s theorem about the convexity of the range of an R-valued vector measure Fin terms of $. We also discuss possible extensions of Gouweleeuw’s results to vector measures with values in infinite-dimensional vector spaces and to unbounded vector measures.