starlikenessconvexityunivalenceequilateral trianglePrimary: 30C45Secondary: 30E20Let Δ be an equilateral triangle, we define the Cauchy transform of the normalized two-dimensional Lebesgue measure μ on Δ by F(z)=∫Δdμ(w)zw. We prove that F is univalent and starlike, but not convex in C...
starlikenessconvexityunivalenceequilateral triangleLet be an equilateral triangle, we define the Cauchy transform of the normalized two-dimensional Lebesgue measure on by . We prove that F is univalent and starlike, but not convex in . In particular, for the regular triangle with vertexes , the ...