Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Certain Novel Subclasses of Analytic and Univalent Functions

  • Irmak, Huseyin (Department of Mathematics Education, Faculty of Education, Baskent University) ;
  • Joshi, Santosh Bhaurao (Department of Mathematics, Walchand College of Engineering) ;
  • Raina, Ravinder Krishen (Department of Mathematics, College of Technology and Engineering, M. P. University of Agriculture and Technology)
  • Received : 2005.07.18
  • Published : 2006.12.23
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Abstract

The purpose of the present paper is to introduce two novel subclasses $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$ and $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$. These results are then appropriately applied to derive similar geometrical properties for the other class $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.

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References

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