# Generalized Close-to-Convexity Related with Bounded Boundary Rotation

## Main Article Content

### Abstract

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) p_{1}(z) – (m/4 – 1/2) p_{2}(z), m ≥ 2,

and p_{1}, p_{2} are subordinate to strongly Janowski function (1+Az/1+Bz)^{α}, α ∈ (0, 1] and −1 ≤ B < A ≤ 1. The class P_{α,m}[A, B] is used to define Vα,m[A, B] and Tα,m[A, B; 0; B_{1}], B_{1} ∈ [−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.

## Article Details

### References

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