A generalization of starlike functions of order alpha

Abstract

In this paper, we mainly study the order of q-starlikeness of the well-known basic hypergeometric function. In addition, we obtain the Bieberbach-type problem for a generalized class of starlike functions. We also discuss the Fekete-szegö and the Hankel determinant problems for the same class of functions.

Some General Classes of q-Starlike Functions Associated with the Janowski Functions

“…in Definition 8, we obtain the class S * q (α), which was introduced and studied by Agrawal and Sahoo [23].…”

Bohr Radius Problems for Some Classes of Analytic Functions Using Quantum Calculus Approach

“…Let f ∈ S * q (α). Proceeding as in proof of [16] (Theorem 1.3, p. 8), it is easy to see that coefficients bound for the function φ(z) = ∑ ∞ n=1 φ n z n are given by…”

“…is the class of q-starlike functions of order α, introduced by Agrawal and Sahoo [16]. Motivated by the authors in [16], Agrawal [17] defined a q-analog of convex functions of order α, 0…”

Applications of a q-Salagean type operator on multivalent functions

“…(ii) For p = 1, m = 0, k = 0, and γ ∈ C\{0}, the class k-US(q, γ , m, p) reduces to the class S * q (γ ) studied by Seoudy and Aouf [27]. (iii) For p = 1, m = 0, k = 0, and γ = 1 1-α , with 0 ≤ α < 1, the class k-US(q, γ , m, p) reduces to the class S * q (α) studied by Agrawal and Sahoo [2]. (iv) For p = 1, m = 0, q → 1, and γ = 1 1-α , with 0 ≤ α < 1, the class k-US(q, γ , m, p) reduces to the class SD(k, α) studied by Shams et al [28].…”