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Some properties of certain analytic functions. (English) Zbl 1139.30306

Summary: Let \({\mathcal A}_p\) be the class of certain analytic functions \(f(z)\) in the open unit disk \(\mathbb U\). For \(f(z)\in{\mathcal A}_p\), a subclass \({\mathcal A}_p(\alpha,\beta,\gamma,j)\) of \({\mathcal A}_p\) is introduced. The object of the present paper is to discuss some properties of functions \(f(z)\) belonging to class \(A_p(\alpha,\beta,\gamma;j)\).

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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References:

[1] Z.-G. Wang, C.-Y. Gao, and S.-M. Yuan, “On the univalency of certain analytic functions,” Journal of Inequalities in Pure and Applied Mathematics, vol. 7, no. 1, article 9, pp. 4, 2006. · Zbl 1131.30327
[2] D. J. Hallenbeck and T. H. MacGregor, Linear Problems and Convexity Techniques in Geometric Function Theory, vol. 22 of Monographs and Studies in Mathematics, Pitman, Boston, Mass, USA, 1984. · Zbl 0581.30001
[3] I. S. Jack, “Functions starlike and convex of order \alpha ,” Journal of the London Mathematical Society. Second Series, vol. 3, pp. 469-474, 1971. · Zbl 0224.30026
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