A NOTE ON CONVEXITY OF CONVOLUTIONS OF HARMONIC MAPPINGS
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In this paper, we study right half-plane harmonic mappings f0 and f, where f0 is fixed and f is such that its dilatation of a conformal automorphism of the unit disk. We obtain a sufficient condition for the convolution of such mappings to be convex in the direction of the real axis. The result of the paper is a generalization of the result of by Li and Ponnusamy [11], which itself originates from a problem posed by Dorff et al. in [7].
Abstract
In this paper, we study right half-plane harmonic mappings f0 and f, where f0 is fixed and f is such that its dilatation of a conformal automorphism of the unit disk. We obtain a sufficient condition for the convolution of such mappings to be convex in the direction of the real axis. The result of the paper is a generalization of the result of by Li and Ponnusamy [11], which itself originates from a problem posed by Dorff et al. in [7].
참고문헌 (12)
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