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The Fekete-Szegő problem for a class of analytic functions defined by Dziok-Srivastava operator. (English) Zbl 1276.30022
In 1991, S. Kanas and A. Wisniowska [J. Comput. Appl. Math. 105, No.1–2, 327–336 (1999; Zbl 0944.30008); Rev. Roum. Math. Pures Appl. 45, No.4, 647–657 (2000; Zbl 0990.30010)] introduced the notion of \(k\)-uniform convexity and \(k\)-starlikeness. Next, R. Bharati, R. Parvatham and A. Swaminathan generalized this notion by introducing the idea of \(k\)-starlikeness and \(k\)-uniform convexity of order \(\gamma\) [Tamkang J. Math. 28, No. 1, 17–32 (1997; Zbl 0898.30010)]. Using the operator introduced by J. Dziok and H. M. Srivastava [Appl. Math. Comput. 103, No.1, 1–13 (1999; Zbl 0937.30010)], the authors define the classes related to \(k\)-uniform convexity and \(k\)-starlikeness of order \(\gamma\). The Fekete-Szegő problem for defined classes is solved.

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