Abstract
In this investigation, the authors prove coefficient bounds, distortion inequalities for fractional calculus of a family of multivalent functions with negative coefficients, which is defined by means of a certain nonhomogenous Cauchy-Euler differential equation.
Highlights
Introduction and DefinitionsLet Tn p denote the class of functions f z of the form ∞f z zp − akzk ak ≥ 0; n, p ∈ N {1, 2, 3, . . .}, which are analytic and multivalent in the unit disk U {z : z ∈ C and |z| < 1}
1−δ dξ δ>0, 1.2 where f z is an analytic function in a -connected region of the z-plane containing the origin and the multiplicity of z − ξ δ−1 is removed by requiring log z − ξ to be real when z − ξ > 0
The class Snδ,p λ, α denote the subclass of Tn p consisting of functions f z which satisfy
Summary
F z zp − akzk ak ≥ 0; n, p ∈ N {1, 2, 3, . . .} , 1.1 knp which are analytic and multivalent in the unit disk U {z : z ∈ C and |z| < 1}. F z zp − akzk ak ≥ 0; n, p ∈ N {1, 2, 3, . . .} , 1.1 knp which are analytic and multivalent in the unit disk U {z : z ∈ C and |z| < 1}. The fractional calculus are defined as follows e.g., 1, 2. 1−δ dξ δ>0 , 1.2 where f z is an analytic function in a -connected region of the z-plane containing the origin and the multiplicity of z − ξ δ−1 is removed by requiring log z − ξ to be real when z − ξ > 0
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