A coefficient inequality for a subclass of the Caratheodory functions defined using conical domains
For 0   k(2)((u - 1)(2) + v(2)), u > 0}. Let q(k)(z) be the Riemann map of U := {z is an element of C : |z|   0. Let P(q(k)) be the class of analytic functions h(z) subordinate in U to q(k)(z) and represented by h(z) = 1 + b(1)z + b(2)z(2) + ..., (2 is an element of U). Sharp estimates for |b(2) - ub(1)(2) (- infinity < u < infinity) are found in this note. This result improves upon an estimate of Kanas in terms of both bounds and ranges of the parameter u [S. Kanas, Coefficient estimates in subclasses of the Caratheodory class related to conical domains, Acta Math. Univ. Comenianae LXXIV 2 (2005) 149-161]. (C) 2011 Elsevier Ltd. All rights reserved.
caratheodory function univalent function k-uniformly convex function jacobi elliptic integral