COEFFICIENT BOUNDS FOR A CERTAIN SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH THE KOEBE FUNCTION

Authors

  • Sidik Rathi Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia
  • Shaharuddin Cik Soh Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia
  • Ajab Akbarally Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia

DOI:

https://doi.org/10.24191/mjoc.v3i2.4601

Keywords:

Close-to-convex Functions, Coefficient Bounds, Koebe Function, Representation Theorem, Univalent Functions

Abstract

We consider here the functions 1.jpg which are analytic and univalent in the open unit disc 2.jpg normalized by  3.jpg and 4.jpg. By 5.jpg, we denote a new subclass of close-to-convex function such that 6.jpg for which 7.jpg and 8.jpg. In this paper, we give the representation theorem and obtain the coefficient bounds for functions in 5.jpg.

References

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Kaplan, W. (1952). Close-to-convex schlicht function. Michigan Mathematical Journal, 1.

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Mohamad, D. (1998). Function whose derivative maps the unit disc into a half plane. PhD Thesis. University of Wales Swansea, UK.

Silverman, H., & Silvia, E. M. (1996). On α-close-to-convex Functions. Publicationes Mathematicae Debrecen, 49, 532-537.

Soh, S. C., & Mohamad. D. (2008). Coefficient bounds for certain classes of close-to-convex functions. International Journal of Mathematical Analysis, Vol. 2, No. 27, 1343-1351.

Yahya, A., Soh, S. C. & Mohamad, D. (2012). Some extremal properties of a generalised Sakaguchi class of cnalytic functions. Proceedings of the 20th National Symposium on Mathematical Sciences.

Published

2018-12-01

How to Cite

Sidik Rathi, Shaharuddin Cik Soh, & Ajab Akbarally. (2018). COEFFICIENT BOUNDS FOR A CERTAIN SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH THE KOEBE FUNCTION. Malaysian Journal of Computing, 3(2). https://doi.org/10.24191/mjoc.v3i2.4601