A Class of Univalent Functions with Negative Coefficients defined by Hadamard Product with Komatu Integral Operator

Authors

  • T. N. Shanmugam Department of Mathematics, College of Engineering Guindy, Anna University, Chennai, Tamilnadu
  • C. Ramachandran Department of Mathematics, University College of Engineering Villupuram, Anna University, Chennai, Tamilnadu
  • R. Ambrose Prabhu Department of Mathematics, College of Engineering Guindy, Anna University, Chennai, Tamilnadu

DOI:

https://doi.org/10.26713/cma.v4i1.162

Keywords:

Univalent function, Hadamard product, Extreme point, Komatu integral operator, Distortion theorem, Fractional calculus

Abstract

In our paper, we study a class $SRA(\lambda, \beta, \alpha, \mu, \theta)$ which consists of analytic and univalent functions with negative coefficients in the open unit disk $\mathbb{U}=\{z:| z | < 1 \}$ defined by Hadamard product (or convolution) with Komatu integral operator, we obtain coefficient bounds and exterior points for this class. Also Distortion Theorem using Fractional Calculus techniques and some results for this class are obtained.
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Issue

Vol. 4 No. 1 (2013)

Section

Research Article

License

Creative Commons Licence 4.0 by

How to Cite

Shanmugam, T. N., Ramachandran, C., & Prabhu, R. A. (2013). A Class of Univalent Functions with Negative Coefficients defined by Hadamard Product with Komatu Integral Operator. Communications in Mathematics and Applications, 4(1), 49-59. https://doi.org/10.26713/cma.v4i1.162