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For normalized harmonic functions f(z) = h(z) + g(z) in the open unit disk, a criterion on the analytic part h(z) for f(z) to be p-valent and sense-preserving is discussed. Furthermore, several illustrative examples and images of f(z) satisfying the obtained condition are enumerated. Publisher's Version

Let A_n be the class of functions f(z) which are analytic in the open unit disk U} with f(0)=0, f'(0)=1, f"(0)=f"'(0)=...=f^{(n)}=0 and f^{(n+1)}\neq0. Applying the results due to S. S. Miller (J. Math. Anal. Appl. 65(1978), 289-305), some interesting starlikeness problems concerned with subordinations are discussed. The results in the paper are extensions of results by M. Obradovi\'c (Hokkaido Math. J. 27(1998), 329-335).