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Generalized k‐Uniformly Close‐to‐Convex Functions Associated with Conic Regions

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  • Khalida Inayat Noor

Abstract

We define and study some subclasses of analytic functions by using a certain multiplier transformation. These functions map the open unit disc onto the domains formed by parabolic and hyperbolic regions and extend the concept of uniformly close‐to‐convexity. Some interesting properties of these classes, which include inclusion results, coefficient problems, and invariance under certain integral operators, are discussed. The results are shown to be the best possible.

Suggested Citation

  • Khalida Inayat Noor, 2012. "Generalized k‐Uniformly Close‐to‐Convex Functions Associated with Conic Regions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:274985
    DOI: 10.1155/2012/274985
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    References listed on IDEAS

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    1. Stanisława Kanas, 2003. "Techniques of the differential subordination for domains bounded by conic sections," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-12, January.
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