Convolution of some slanted half-plane mappings with harmonic strip mappings

Abstract

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