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ABSTRACT Let Δ be an equilateral triangle, we define the Cauchy transform of the normalized two-dimensional Lebesgue measure μ on Δ by . We prove that F is univalent and… Click to show full abstract
ABSTRACT Let Δ be an equilateral triangle, we define the Cauchy transform of the normalized two-dimensional Lebesgue measure μ on Δ by . We prove that F is univalent and starlike, but not convex in . In particular, for the regular triangle with vertexes , the Cauchy transform is convex of order in .
Keywords:
convexity cauchy;
cauchy transform;
transform equilateral;
starlikeness convexity;
equilateral triangle
Journal Title: Complex Variables and Elliptic Equations
Year Published: 2019
Link to full text (if available)
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Journal Title: Complex Variables and Elliptic Equations
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!