Convex combinations of nilpotent triangular norms

Convex combinations of harmonic shears of slit mappings

‎In this paper‎, ‎we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings‎. ‎Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived‎. ‎Several examples of univalent harmonic mappings constructed by using these methods are presented to illustrate...

Generated triangular norms

Archimedean components of triangular norms

The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordina...

Convex Sets and Convex Combinations

Convexity is one of the most important concepts in a study of analysis. Especially, it has been applied around the optimization problem widely. Our purpose is to define the concept of convexity of a set on Mizar, and to develop the generalities of convex analysis. The construction of this article is as follows: Convexity of the set is defined in the section 1. The section 2 gives the definition...

Pinchings and Norms of Scaled Triangular Matrices 1 Pinchings and Norms of Scaled Triangular Matrices

Suppose U is an upper-triangular matrix, and D a nonsingular diagonal matrix whose diagonal entries appear in nondescending order of magnitude down the diagonal. It is proved that kD UDk kUk for any matrix norm that is reduced by a pinching. In addition to known examples { weakly unitarily invariant norms { we show that any matrix norm de ned by kAk def = max x 6=0; y 6=0 Re (x Ay) (x) (y) ; wh...