Bohr's Phenomenon for Some Univalent Harmonic Functions

In 1914, Bohr proved that there is an r(0) is an element of (0, 1) such that if a power series Sigma(infinity)(m=0) c(m) z(m) is convergent in the open unit disc and vertical bar Sigma(infinity)(m=0) c(m) z(m)vertical bar < 1 then, Sigma(infinity)(m=0) vertical bar c(m) z(m)vertical bar < for vertical bar z vertical bar < r(0). The largest value of such r(0) is called the Bohr radius. In this article, we find Bohr radius for some univalent harmonic mappings having different dilatations. We also compute the Bohr radius for functions that are convex in one direction.