Abstract
For −1≤B<A≤1, let \(\mathcal {S}^{*}(A,B)\) denote the class of normalized analytic functions \(f(z)= z+{\sum }_{n=2}^{\infty }a_{n} z^{n}\) in |z|<1 which satisfy the subordination relation z f ′(z)/f(z)≺(1 + A z)/(1 + B z) and Σ∗(A,B) be the corresponding class of meromorphic functions in |z|>1. For \(f\in \mathcal {S}^{*}(A,B)\) and λ>0, we shall estimate the absolute value of the Taylor coefficients a n (−λ,f) of the analytic function (f(z)/z)−λ. Using this we shall determine the coefficient estimate for inverses of functions in the classes \(\mathcal {S}^{*}(A,B)\) and Σ∗(A,B).
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Acknowledgements
The authors would like to thank Prof. S. Ponnusamy for useful discussions and careful reading of the paper. The authors also thank him for bringing paper [15] to their attention. The first author thanks University Grants Commission for the financial support through UGC-SRF Fellowship. The second author also thanks SRIC, IIT Kharagpur for their support.
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ALI, M.F., VASUDEVARAO, A. Coefficient estimates of negative powers and inverse coefficients for certain starlike functions. Proc Math Sci 127, 449–462 (2017). https://doi.org/10.1007/s12044-017-0328-5
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DOI: https://doi.org/10.1007/s12044-017-0328-5