Toeplitz matrices whose elements are the coefficients of starlike and close-to-convex functions. (English) Zbl 1386.30024
Bull. Malays. Math. Sci. Soc. (2) 40, No. 4, 1781-1790 (2017); retraction note ibid. 41, No. 2, 1151 (2018).
Summary: Let \(f\) be analytic in \(D=\{z: |z|< 1\}\) with \(f(z)=z+\sum_{n=2}^{\infty}a_{n}z^{n}\). Suppose that \(S^*\) is the class of starlike functions, and \(K\) is the class of close-to-convex functions. The paper instigates a study of finding estimates for Toeplitz determinants whose elements are the coefficients \(a_{n}\) for \(f\) in \(S^*\) and \(K\).
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
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