CONVOLUTION OF SOME SLANTED HALF-PLANE MAPPINGS WITH HARMONIC STRIP MAPPINGS

CONVOLUTION OF SOME SLANTED HALF-PLANE MAPPINGS WITH HARMONIC STRIP MAPPINGS

P. Sharma, O Mishra

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Abstract

In this paper, we show that the convolution of generalized half-plane map- ping and harmonic vertical strip mapping with dilatation eiθ zn (n ∈ N, θ ∈ R) is convex in a particular direction and also solve the problem proposed by Z. Liu et al. [Convolu- tions of harmonic half-plane mappings with harmonic vertical strip mappings, Filomat, 31 (2017), no. 7, 1843–1856].

Keywords

Harmonic vertical strip mappings, slanted half-plane mappings, convolution.