The conic structure of the convex cone of non-negative operator convex functions on (0,∞) (also on (−1, 1)) is clarified. We completely determine the extreme rays, the closed faces, and the simplicial closed faces of this convex cone.

Let X and Y be real Banach spaces, K be a nonempty convex subset of X , and C : K → 2Y be a multifunction such that for each u ∈ K , C(u) is a proper, closed and convex cone with intC(u) 6= ∅, where intC(u) denotes the interior of C(u). Given the mappings T : K → 2L(X,Y ,A : L(X, Y )→ L(X, Y ), f1 : L(X, Y )×K×K → Y , f2 : K×K → Y , and g : K → K , we introduce and consider the generalized impl...

The global error bound estimation for the generalized nonlinear complementarity problem over a closed convex cone GNCP is considered. To obtain a global error bound for the GNCP, we first develop an equivalent reformulation of the problem. Based on this, a global error bound for the GNCP is established. The results obtained in this paper can be taken as an extension of previously known results.

‎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 celebrated Farkas lemma originated in Farkas (1902) provides us an attractively simple and extremely useful characterization for a linear inequality to be a consequence of a linear inequality system on the Euclidean space Rn . This lemma has been extensively studied and extended in many directions, including conic systems (linear, sublinear, convex), infinite/semi-infinite convex inequality...

Abstract In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) preordered by a not necessarily solid (and pointed) convex cone. It well-known that there are many examples ordering cone has an empty (topological/algebraic) interior, for instance in optimal control, approximation theory, duality theory. Our aim consider Pareto-type solu...

Various types of φA-spaces (X,D; {φA}A∈〈D〉) are simply G-convex spaces. Various types of generalized KKM maps on φA-spaces are simply KKM maps on G-convex spaces. Therefore, our G-convex space theory can be applied to various types of φAspaces. As such examples, we obtain KKM type theorems and a very general fixed point theorem on φA-spaces. RESUMEN Varios tipos de φA-espacios (X,D; {φA}A∈〈D〉) ...

A sectorial matrix is an n×n whose numerical range contained in open half-plane, and such matrices have many nice properties. In particular, the subset of strictly accretive a convex cone space matrices, results related to positive definite recently been generalized this cone. Moreover, used define phases matrix, these can be angularly bound eigenvalues by majorization-type inequalities similar...

Abstract. In this paper, we define the notion of C*-affine maps in the unital *-rings and we investigate the C*-extreme points of the graph and epigraph of such maps. We show that for a C*-convex map f on a unital *-ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C*-face of the epigraph of f. Moreover, we prove som...

in this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in cat(0) spaces as well as in uced banach spaces. moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...