Coefficient inequalities for a new class of univalent functions

Maslina Darus, R. W. Ibrahim

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In the present article, a new class ∑ α , 0 ≤ α < 1, of analytic and univalent functions f: U → C where U is an open unit disk, satisfying the standard normalization f(0) = f′(0) - 1 = 0 is considered. Assume that f ∑ α takes the form such that A 0,0 = 0 and A 1,0 = 1. Also, we define the family Co(p), where p (0, 1), of functions f: U →C that satisfy the following conditions: (i) f ∑ α is meromorphic in U and has a simple pole at the point p. (ii) f(0) = f′(0) - 1 = 0. (iii) f maps U conformally onto a set whose complement with respect toC is convex. We call such functions concave univalent functions. We prove some coefficient estimates for functions in this class when f has the expansion The second part of the article concerns some properties of a generalized Sǎlǎgean operator for functions in ∑ α . Moreover, a result on subordination for the functions f ∑ α is given.

Original languageEnglish
Pages (from-to)221-229
Number of pages9
JournalLobachevskii Journal of Mathematics
Volume29
Issue number4
DOIs
Publication statusPublished - Oct 2008

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Coefficient Inequalities
Univalent Functions
Coefficient Estimates
Subordination
Concave function
Meromorphic
Unit Disk
Normalization
Pole
Analytic function
Complement
Class
Operator

Keywords

  • Concave functions
  • Convex set
  • Meromorphic univalent functions
  • Sǎlǎgean operator

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Coefficient inequalities for a new class of univalent functions. / Darus, Maslina; Ibrahim, R. W.

In: Lobachevskii Journal of Mathematics, Vol. 29, No. 4, 10.2008, p. 221-229.

Research output: Contribution to journalArticle

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