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We first prove that the convolution of a normalized right half-plane mapping with another subclass of normalized right half-plane mappings with the dilatation [...] −z(a+z)/(1+az) $-z(a+z)/(1+az)$ is CHD (convex in the horizontal direction) provided [...] a=1 $a=1$ or [...] −1≤a≤0 $-1\le a\le 0$ . Secondly, we give a simply method to prove the convolution of two special subclasses of harmonic univalent mappings in the right half-plane is CHD which was proved by Kumar et al. [1, Theorem 2.2]. In addition, we derive the convolution...