‎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...

We find the sharp radius of uniformly convex γ-spirallikeness for Nν(z)=az2Jν″(z)+bzJν′(z)+cJν(z) (here Jν(z) is Bessel function first kind order ν) with three different kinds normalizations Nν(z). As an application, we derive sufficient conditions on parameters functions to be and, consequently, generate examples uniform γ-spirallike via Results are well-supported by relevant graphs and tables.

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

Let Sk be the set of separable states on B(C ⊗ C) admitting a representation as a convex combination of k pure product states, or fewer. If m > 1, n > 1, and k ≤ max (m,n), we show that Sk admits a subset Vk such that Vk is dense and open in Sk, and such that each state in Vk has a unique decomposition as a convex combination of pure product states, and we describe all possible convex decomposi...

Linear programming is a very powerful technique, applicable not only in optimization, but in combinatorial theory. For example, we will see that König’s theorem (Lecture 1,Theorem 2) is an instance of the principle of (integral) linear programming duality. In this section, we remind ourselves of the basic relevant concepts. Given a collection of vectors v1, v2, . . . .vm ∈ R their linear combin...