Certain classes of p-valent analytic functions with negative coefficients and (λ, P)-starlike with respect to certain points

Adnan Ghazy Alamoush, Maslina Darus

Research output: Contribution to journalArticle

Abstract

In this article, we consider classes S*sc, λ(p, α, β), S*c, λ(p, α, β), and S*sc, λ(p, α, β) of p-valent analytic functions with negative coefficients in the unit disk. They are, respectively, (λ, p)-starlike with respect to symmetric points, (λ, p)-starlike with respect to conjugate points, and (λ, p)-starlike with respect to symmetric conju-gate points. Necessary and sufficient coefficient conditions for functions f belonging to these classes are obtained. Several properties such as the coefficient estimates, growth and distortion theorems, extreme points, radii of starlikeness, convexity, and integral operator are studied.

Original languageEnglish
Pages (from-to)35-49
Number of pages15
JournalBuletinul Academiei de Stiinte a Republicii Moldova. Matematica
Volume79
Issue number3
Publication statusPublished - 2015

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P-valent Functions
Analytic function
Coefficient
Distortion Theorem
Conjugate points
Starlikeness
Coefficient Estimates
Extreme Points
Integral Operator
Unit Disk
Convexity
Radius
Sufficient
Necessary
Class

Keywords

  • P-valent functions
  • Salagean operator
  • Starlike with respect to symmetric points
  • Univalent functions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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N2 - In this article, we consider classes S*sc, λ(p, α, β), S*c, λ(p, α, β), and S*sc, λ(p, α, β) of p-valent analytic functions with negative coefficients in the unit disk. They are, respectively, (λ, p)-starlike with respect to symmetric points, (λ, p)-starlike with respect to conjugate points, and (λ, p)-starlike with respect to symmetric conju-gate points. Necessary and sufficient coefficient conditions for functions f belonging to these classes are obtained. Several properties such as the coefficient estimates, growth and distortion theorems, extreme points, radii of starlikeness, convexity, and integral operator are studied.

AB - In this article, we consider classes S*sc, λ(p, α, β), S*c, λ(p, α, β), and S*sc, λ(p, α, β) of p-valent analytic functions with negative coefficients in the unit disk. They are, respectively, (λ, p)-starlike with respect to symmetric points, (λ, p)-starlike with respect to conjugate points, and (λ, p)-starlike with respect to symmetric conju-gate points. Necessary and sufficient coefficient conditions for functions f belonging to these classes are obtained. Several properties such as the coefficient estimates, growth and distortion theorems, extreme points, radii of starlikeness, convexity, and integral operator are studied.

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