Applications of fractional calculus to $ k $-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $

Authors

  • Ajab Akbarally
  • Maslina Darus

DOI:

https://doi.org/10.5556/j.tkjm.38.2007.81

Abstract

A new subclass of analytic functions $ k-SP_\lambda(\alpha) $ is introduced by applying certain operators of fractional calculus to $k$-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $. Some theorems on coefficient bounds and growth and distortion theorems for this subclass are found. The radii of close to convexity, starlikeness and convexity for this subclass is also derived.

Author Biographies

Ajab Akbarally

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia,43600 UKM Bangi Selangor D. Ehsan, Malaysia.

Maslina Darus

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor D. Ehsan, Malaysia.

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Published

2007-06-30

How to Cite

Akbarally, A., & Darus, M. (2007). Applications of fractional calculus to $ k $-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $. Tamkang Journal of Mathematics, 38(2), 103-109. https://doi.org/10.5556/j.tkjm.38.2007.81

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Papers

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