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Differential subordinations concerning starlike functions

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Abstract

Denote byS * (⌕), (0≤⌕<1), the family consisting of functionsf(z)=z+a 2z2+...+anzn+... that are analytic and starlike of order ⌕, in the unit disc ⋎z⋎<1. In the present article among other things, with very simple conditions on μ, ⌕ andh(z) we prove the f’(z) (f(z)/z)μ−1<h(z) implies f∈S*(⌕). Our results in this direction then admit new applications in the study of univalent functions. In many cases these results considerably extend the earlier works of Miller and Mocanu [6] and others.

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  1. School of Mathematics, SPIC Science Foundation, 92, G N Chetty Road, 600 017, Madras, India

    S Ponnusamy

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  1. S Ponnusamy
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Ponnusamy, S. Differential subordinations concerning starlike functions. Proc. Indian Acad. Sci. (Math. Sci.) 104, 397–411 (1994). https://doi.org/10.1007/BF02863420

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  • DOI: https://doi.org/10.1007/BF02863420

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