ADV MATH SCI JOURNAL Advances in Mathematics: Scientific Journal 9 (2020), no.1, 445–454 ISSN: 1857-8365 (printed); 1857-8438 (electronic) https://doi.org/10.37418/amsj.9.1.35 ON A SUBCLASS OF UNIVALENT HARMONIC MAPPINGS CONVEX IN THE IMAGINARY DIRECTION DEEPALI KHURANA 1 , SUSHMA GUPTA, AND SUKHJIT SINGH ABSTRACT. In the present article, we consider a class of univalent harmonic mappings, C T =  T c [f ]= f +czf ′ 1+c + f -czf ′ 1+c ; c> 0  and f is convex univalent in D, whose functions map the open unit disk D onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class. 1. I NTRODUCTION A domain Ω ⊂ C is said to be convex if for any two points w 1 and w 2 in Ω, the line segment tw 1 + (1 − t)w 2 (0 ≤ t ≤ 1) lies entirely in Ω. A domain Ω ⊂ C is said to be convex in a direction γ ∈ [0,π), if for all a ∈ C, the set {a + te iγ : t ∈ R} has either empty or connected intersection with Ω. In particular, a domain is convex in the direction of the real (imaginary) axis if every line parallel to the real (imaginary) axis has either an empty or connected intersection with that domain. A function which maps the unit disk D = {z ∈ C : |z | < 1} onto a convex domain or onto a domain convex in a direction γ , is said to be convex function or function convex in direction γ , respectively. In 2008, Muir [3] defined a transformation T c [f ],c> 0 as follows. 1 corresponding author 2010 Mathematics Subject Classification. 30C45, 30C50, 30C55, 30C80. Key words and phrases. Harmonic functions, harmonic univalent, harmonic convex, har- monic starlike, growth and covering theorems, coefficient bound. 445