In this paper, we introduce a new class (Formula presented) (k; γ; ɸ) of harmonic quasiconformal mappings, where k ∈ [0, 1), γ ∈ [0, π) and ɸ is an analytic function. Sufcient conditions for the linear combinations of mappings in such classes to be in a similar class, and convex in a given direction, are established. In particular, we prove that the images of linear combinations in this class, for special choices of γ and ɸ, are convex.
- Convex in one direction
- Harmonic K-quasiconformal mapping
- Linear combination
- Univalent harmonic mapping