Majorization by starlike functions of complex order

Abstract

The authors investigate several majorization problems involving starlike and convex functions of complex order as well as functions belonging to a certain class R(h, y) which they introduce here. Relevant connections of the main results obtained in this paper with those given by earlier workers on the subject are also pointed out.

Majorization properties for a new subclass of θ-spiral functions of order γ

“…Taking λ = 1, m = 0, q = 2, s = 1, α 1 = β 1 = 1 and α 2 = 1 in Corollary 2.2, we obtain the result of Altintas et al [17].…”

“…Also, majorization problems for starlike functions of complex order have recently been investigated by Altintas et al [17], Goyal et al [18,19], and Goswami et al [20,21]. Motivated by these works, in this paper, we investigate a majorization problem for the class S m,l p,q,s,λ (γ, θ).…”

On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

“…A majorization properties for the class of starlike functions of complex order γ and the class of convex functions of complex order γ (γ ∈ C * ) has been investigated by Altintaş et al [1] and MacGregor [19] has also studied the same problem for the classes S and C , respectively. Recently, Goyal and Goswami [6], and Goyal et al [7] generalized these results for different function classes.…”

Majorization problems for classes of analytic functions

“…Recently Altintas et al [4] investigated a majorization problem for the class C * (γ) and Goyal and Goswami [5] generalized these results for the class of analytic functions involving fractional operator. In this paper we investigated a majorization problem for the class S c m (A, B; γ) associated with Bessel functions and point out some special cases of our result.…”