Linear combinations of univalent harmonic mappings convex in the direction of the imaginary axis

Raj Kumar; Sushma Gupta; Sukhjit Singh

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arXiv · 1306.1727

Linear combinations of univalent harmonic mappings convex in the direction of the imaginary axis

Raj Kumar·Sushma Gupta·Sukhjit Singh

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Abstract

In the present paper, we introduce a family of univalent harmonic functions, which map the unit disk onto domains convex in the direction of the imaginary axis. We find conditions for the linear combinations of mappings from this family to be univalent and convex in the direction of the imaginary axis. Linear combinations of functions from this family and harmonic mappings obtained by shearing of analytic vertical strip maps are also studied.

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Raj Kumar, Sushma Gupta, Sukhjit Singh. 2013-06-07. Linear combinations of univalent harmonic mappings convex in the direction of the imaginary axis. https://arxiv.org/abs/1306.1727

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