Open AccessGeneralized Close-to-Convexity Related with Bounded Boundary Rotation
Author(s) -
Khalida İnayat Noor,
Muhammad Aslam Noor,
Muhammad Uzair Awan
Publication year - 2021
Publication title -
international journal of analysis and applications
Language(s) - English
Resource type - Journals
ISSN - 2291-8639
DOI - 10.28924/2291-8639-19-2021-890
Subject(s) - convexity , mathematics , bounded function , boundary (topology) , rotation (mathematics) , function (biology) , combinatorics , class (philosophy) , radius , unit disk , analytic function , pure mathematics , mathematical analysis , geometry , computer security , evolutionary biology , artificial intelligence , computer science , financial economics , economics , biology
The class Pα,m[A, B] consists of functions p, analytic in the open unit disc E with p(0) = 1 and satisfyp(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.