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On quasi-convex functions and related topics

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  • Khalida Inayat Noor

Abstract

Let S be the class of functions f which are analytic and univalent in the unit disc E with f ( 0 ) = 0 , f ′ ( 0 ) = 1 . Let C , S * and K be the classes of convex, starlike and close-to-convex functions respectively. The class C * of quasi-convex functions is defined as follows: Let f be analytic in E and f ( 0 ) , f ′ ( 0 ) = 1 . Then f ϵ C * if and only if there exists a g ϵ C such that, for z ϵ E Re ( z f ′ ( z ) ) ′ g ′ ( z ) > 0 . In this paper, an up-to-date complete study of the class C * is given. Its basic properties, its relationship with other subclasses of S , coefficient problems, arc length problem and many other results are included in this study. Some related classes are also defined and studied in some detail.

Suggested Citation

  • Khalida Inayat Noor, 1987. "On quasi-convex functions and related topics," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 10, pages 1-18, January.
    • Handle: RePEc:hin:jijmms:491830
    DOI: 10.1155/S0161171287000310
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    Cited by:

    1. Amit Soni & Shashi Kant, 2013. "Some Inclusion Relations Associated with Generalized Fractional Differintegral Operator," International Journal of Analysis, Hindawi, vol. 2013, pages 1-6, March.

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