APPLIED MATHEMATICS AND COMPUTATION, cilt.357, ss.374-378, 2019 (SCI-Expanded)
Let consider A(p) denoting a class of analytical functions defined as f(z) = z(p) + a(p)+ (1)z(p+1) + center dot center dot center dot + a(p+n)z(p+n) + center dot center dot center dot and p-valent in unit disc U = {z vertical bar vertical bar z vertical bar < 1}. f (z) is an element of A(p) is expressed to be p-valently starlike in U if there is a positive figure rho fulfilling rho < vertical bar z vertical bar < 1, Re(zf'(z)/f(z)) > 0, and integral(2 pi)(0) Re(zf'(z)/f(z))d theta = 2p pi, z = re(i theta), rho < r < 1. Let us consider S*(p) denoting the family of f(z) in A(p), being regular and p-valently starlike in U. It was proved by Goodman [3] that f (z) is an element of S*(p) is at most p-valent in U.