Graphing Examples of Starlike and Convex Functions of order β

Authors

Hameed Ur Rehman, School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 Selangor Darul Ehsan, Malaysia\\ Center for Language and Foundation Studies, A’ Sharqiyah University, Post Box No. 42, Post Code No. 400 Ibra, Sultanate of OmanFollow
Maslina Darus, School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 Selangor Darul Ehsan, MalaysiaFollow
Jamal Salah, College of Applied and Health Sciences, A’ Sharqiyah University, Post Box No. 42, Post Code No. 400 Ibra, Sultanate of OmanFollow

Author Country (or Countries)

Malaysia

Abstract

In this paper, we introduce and investigate two subclasses H∗b(n,b,f ) and Kb (n,b,f ) of analytic functions with negative coefficients of order b in the unit disk D. Silverman [6] determined certain coefficient inequalities and distortion theorems for univalent functions with negative coefficients that are starlike S(a), and convex K(a) of order a respectively. We also obtain the same coefficient inequalities and distortion theorem for such univalent functions with negative coefficients. We point out that the coefficient estimates up to z9 are enough to get the graphs of starlike and convex functions. Here in the sequel we give some examples, estimation and the graphical representation of such univalent functions by using the complex tool [8].

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/journal/100305

Recommended Citation

Ur Rehman, Hameed; Darus, Maslina; and Salah, Jamal (2018) "Graphing Examples of Starlike and Convex Functions of order β," Applied Mathematics & Information Sciences: Vol. 12: Iss. 3, Article 5.
DOI: http://dx.doi.org/10.18576/journal/100305
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss3/5