Abstract
Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the classTSml(α,β,γ). In particular, we obtain integral means inequalities for the functionfthat belongs to the classTSml(α,β,γ)in the unit disc.
Highlights
Let A denote the class of functions of the form ∞fz z anzn n2 which are analytic in the open unit disc U {z : z ∈ C, |z| < 1} and normalized by f 0 f 0 − 1 0
Fz z anzn n2 which are analytic in the open unit disc U {z : z ∈ C, |z| < 1} and normalized by f 0 f 0 − 1 0
It is known the definition of the Hadamard product
Summary
Denote by T the subclass of A consisting of functions of the form f z z − |an|zn, n2 introduced and studied by Silverman 1. 1.8 and is said to be in the class UCV α, β , uniformly β-convex functions if it satisfies the condition. Motivated by Altintas et al , Murugusundaramoorthy and Srivastava , and Murugusundaramoorthy and Magesh , we define a new subclass uniformly starlike functions of complex order. Βm, α, γ, and β the class T Slm α, β, γ , leads to various new subclasses of starlike functions of complex order. The main object of this paper is to study some usual properties of the geometric function theory such as the coefficient bound, extreme points, radii of close to convexity, starlikeness, and convexity for the class T Slm α, β, γ. We obtain neighborhood results and integral means inequalities for aforementioned class
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