Coefficient inequalities for strongly close-to-convex functions

[摘要] Let f(z) = z + a(2)z(2) + a(3)z(3) + ... be a normalized strongly close-to-convex function of order alpha > 0 defined on the unit disk D. This means that there is a normalized convex univalent function phi and beta is an element of R such that \arg f'(z)\e(i beta)phi'(z)\ < alpha pi/2 for z is an element of D. Then \a(3) - a(2)(2)\ + 1/3\a(x)\(2) less than or equal to 1/3(1 + 4 alpha + 2 alpha(2)) and \a(3) - 2/3a(2)(2)\ + 2/3\a(2)\(2) less than or equal to 1/3(3 + 4 alpha + 2 alpha(2)) with equality if and only if f is a rotation of F-alpha(z) = 1/2(1 + alpha)[(1 + z/1 - z)(1 + alpha) = 1]. (C) 1997 Academic Press.

[发布日期] 1997-01-15