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In this paper, we introduce a new class SH šk, g; fŽ of harmonic quasiconformal mappings, where k A ½0, 1Ž, g A ½0, pŽ and f is an analytic function. Sufficient 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 g and f, are convex.