Generalized Close-to-Convexity Related with Bounded Boundary Rotation

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Khalida Inayat Noor, Muhammad Aslam Noor, Muhammad Uzair Awan


The class Pα,m[A, B] consists of functions p, analytic in the open unit disc E with p(0) = 1 and satisfy

p(z) = (m/4 + ½) p1(z) – (m/4 – 1/2) p2(z), m ≥ 2,

and p1, p2 are subordinate to strongly Janowski function (1+Az/1+Bz)α, α ∈ (0, 1] and −1 ≤ B < A ≤ 1. The class Pα,m[A, B] is used to define Vα,m[A, B] and Tα,m[A, B; 0; B1], B1 ∈ [−1, 0). These classes generalize the concept of bounded boundary rotation and strongly close-to-convexity, respectively. In this paper, we study coefficient bounds, radius problem and several other interesting properties of these functions. Special cases and consequences of main results are also deduced.

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