New Subclass of Close-to-convex Functions Associated with the Vertical Strip Domains

In the present paper, we introduce the class B-theta (alpha, beta) consisting of functions f, analytic in the unit disc Delta, normalized by the condition f (0) = 0 = f'(0) - 1 and satisfying the following two-sided inequality alpha < Re { f'(z) + 1 + e(i theta)/2 zf ''(z) } < beta (z is an element of Delta),where theta is an element of (-pi, pi], 0 <= alpha < 1 and beta > 1. Integral representation, differential subordination results, coefficient estimates and Fekete-Szego<spacing diaeresis> coefficient functional associated with the k-th (k >= 1) root transform [f(z(k))](1/k) for functions in the class B-theta (alpha, beta), are determined.