On the representation formulas for the functions in class Σ*(𝑝,𝑤₀)

Chang, Yuh Lin

doi:10.1090/S0002-9939-1988-0943077-1

On the representation formulas for the functions in class $\Sigma ^ *(p,w_ 0)$
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Proc. Amer. Math. Soc. 103 (1988), 517-520 Request permission

Abstract:

We prove the converse of J. Miller’s integral representation theorem for functions in the class ${\Sigma ^ * }(p,{w_0})$ of starlike meromorphic univalent functions. As an application we improve the bounds of the modulus. We also observe some properties of the class ${\text {ST}}\left ( P \right ) = { \cup _{w0}}{\Sigma ^ * }\left ( {p,{w_0}} \right )$.

References

James Miller, Starlike meromorphic functions, Proc. Amer. Math. Soc. 31 (1972), 446–452. MR 288267, DOI 10.1090/S0002-9939-1972-0288267-7
James Miller, Convex and starlike meromorphic functions, Proc. Amer. Math. Soc. 80 (1980), no. 4, 607–613. MR 587937, DOI 10.1090/S0002-9939-1980-0587937-5
J. A. Hummel, The coefficients of starlike functions, Proc. Amer. Math. Soc. 22 (1969), 311–315. MR 251209, DOI 10.1090/S0002-9939-1969-0251209-4

Linear problems and convexity techniques