Abstract
For μ∈C, φ a starlike univalent function, the class of functions f that are spiral-like with respect to a boundary point satisfying the subordination 2 μ z f ′ ( z ) f ( z ) + 1 + z 1 − z ≺φ(z),z∈D, is investigated. The integral representation, growth and distortion theorem are proved by relating these functions with Ma and Minda starlike functions. Some earlier results are shown to be a special case of the results obtained.MSC:30C80, 30C45.
Highlights
The class of starlike functions with respect to origin is denoted by S*
1 Introduction and motivation Let D = {z : |z| < } be an open unit disk of the complex plane C and let A be a class of analytic functions f normalized by f ( ) = and f ( ) =
The distortion results for starlike functions with respect to a boundary point were obtained in [, ]
Summary
The class of starlike functions with respect to origin is denoted by S*. Robertson [ ] took a leap forward with the characterization of the class S* and defined the class Sb* of starlike functions with respect to a boundary point. It is the characterization of a function f ∈ Sb = {f (z) = + d z + d z + · · · |f univalent} such that f (D) is starlike with respect to the boundary point f ( ) := limr→ – f (r) = and lies in a half-plane.
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