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Radius Constants for Functions with the Prescribed Coefficient Bounds

Author

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  • Om P. Ahuja
  • Sumit Nagpal
  • V. Ravichandran

Abstract

For an analytic univalent function in the unit disk, it is well-known that for . But the inequality does not imply the univalence of . This motivated several authors to determine various radii constants associated with the analytic functions having prescribed coefficient bounds. In this paper, a survey of the related work is presented for analytic and harmonic mappings. In addition, we establish a coefficient inequality for sense-preserving harmonic functions to compute the bounds for the radius of univalence, radius of full starlikeness/convexity of order   ( ) for functions with prescribed coefficient bound on the analytic part.

Suggested Citation

  • Om P. Ahuja & Sumit Nagpal & V. Ravichandran, 2014. "Radius Constants for Functions with the Prescribed Coefficient Bounds," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, September.
    • Handle: RePEc:hin:jnlaaa:454152
    DOI: 10.1155/2014/454152
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