Abstract
Let A be the set of all analytic functions f defined on the open unit disk D satisfying f(0) = f'(0) − 1 = 0. Let φNe(z) := 1 + z − z3=3 be the recently introduced Carathéodory function which maps the unit circle
where F(z) is some Carathéodory function with special geometries like right/left-half of Bernoulliφs lemniscate, cardioid, lune, eight-shaped, etc. As applications, we establish sufficient conditions for the Ma-Minda family of nephroid starlike functions given by
Acknowledgement
The authors would like to express their gratitude to the anonymous referees for their thoughtful comments and efforts towards improving the paper.
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(Communicated by Stanisława Kanas)
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