Graphing examples of starlike and convex functions of order β

Hameed Ur Rehman, Maslina Darus, Jamal Salah

Research output: Contribution to journalArticle

Abstract

In this paper, we introduce and investigate two subclasses Hβ*(n, b,ϕ) and Kβ(n, b,ϕ) of analytic functions with negative coefficients of order β in the unit disk D. Silverman [6] determined certain coefficient inequalities and distortion theorems for univalent functions with negative coefficients that are starlike S(α), and convex K(α) of order α 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].

Original languageEnglish
Pages (from-to)509-515
Number of pages7
JournalApplied Mathematics and Information Sciences
Volume12
Issue number3
DOIs
Publication statusPublished - 1 May 2018

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Starlike and Convex Functions
Univalent Functions
Coefficient Inequalities
Distortion Theorem
Coefficient
Coefficient Estimates
Graphical Representation
Unit Disk
Analytic function
Graph in graph theory

Keywords

  • Convex functions
  • Distortion theorems
  • Starlike functions
  • Univalent functions

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Graphing examples of starlike and convex functions of order β. / Rehman, Hameed Ur; Darus, Maslina; Salah, Jamal.

In: Applied Mathematics and Information Sciences, Vol. 12, No. 3, 01.05.2018, p. 509-515.

Research output: Contribution to journalArticle

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