Abstract
In the paper we define classes of harmonic starlike functions with respect to symmetric points and obtain some analytic conditions for these classes of functions. Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are also obtained.
Highlights
We denote by H the class of complex-valued harmonic functions in the unit disc U := {z : |z| < r }
Let SH denote the class of functions f ∈ H0, which are orientation preserving and univalent in U
An analytic function f is said to be starlike with respect to symmetric points if: z f 0 (z)
Summary
We denote by H the class of complex-valued harmonic functions in the unit disc U := {z : |z| < r }. In 1956 Sakaguchi [1] introduced the class S ∗∗ of analytic univalent functions in U which are starlike with respect to symmetrical points. An analytic function f is said to be starlike with respect to symmetric points if:. We obtain the classes SH f ∈ SH which are convex in U (r ) or starlike in U (r ) , respectively, for any r ∈ In the present paper we obtain some analytic conditions for defined classes of functions. Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are obtained. (see [7,8])
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.