Program analysis using abstract interpretation has been successfully applied in practice to find runtime bugs or prove software correct. Most abstract domains that are used widely rely on convexity for their scalability. However, the ability to express non-convex properties is sometimes required in order to achieve a precise analysis of some numerical properties. This work combines already know...

We study the relations between boundaries for algebras of holomorphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic functions on an order continuous sequence space X is the unit sphere SX if X is locally c-convex. In particular, it is shown that the unit sphere of the OrliczLorentz sequence space λφ,w i...

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...

We combine a Lagrangian approach inspired by convex and quasiconvex dualities with a penalization approach to mathematical programming. We use the ideas of abstract convexity. We focus our attention on the set of multipliers. We look for an interpretation of multipliers as elements of generalized subdifferentials of the performance function associated with a dualizing parameterization of the gi...

Abstract This paper consider the existence and multiplicity of solutions for the first order Hamiltonian systems satisfying Sturm-Liouville boundary conditions without convexity assumption. The gradient of Hamiltonian function is generalized asymptotically linear. We find critical points of the corresponding functional by verifying the assumptions of Theorems about critical points given by Bart...

We present some properties regarding diffusion and semi-convexity for fuzzy set multifunctions defined on a ring of subsets of an abstract nonvoid space and taking values in the family of all nonvoid closed subsets of a real normed space. Key–Words: diffused, semi-convex, fuzzy set multifunction, non-atomicity, Darboux property, regular, multimeasure, null-additive.

‎Many optimization problems can be reduced to a problem with an increasing and co-radiant objective function by a suitable transformation of variables. Functions, which are increasing and co-radiant, have found many applications in microeconomic analysis. In this paper, the abstract convexity of positive valued affine increasing and co-radiant (ICR) functions are discussed. Moreover, the ...

CONVEXITY RELATED ISSUES FOR THE SET OF HYPERGRAPHIC SEQUENCES Hasmik Sahakyan, Levon Aslanyan Abstract: We consider ( ), the set of all degree sequences of simple hypergraphs with vertices and hyperedges. We show that ( ), which is a subset of the -dimensional + 1-valued grid , is not a convex subset of ; and give a characterization of the convex hull of ( ).