α-Logarithmically convex functions

Maslina Darus, D. K. Thomas

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

For α ≥ 0, we introduce the class Mα of normalised analytic α-logarithmically convex functions defined in the open unit disc D by Re{(1 +zf″ (z)/f′ (z))α (zf′ (z)/f(z))1-α } > 0 For f ∈ Mα, a best possible subordination theorem is obtained which implies that Mα forms a subset of the starlike functions S*. Some extreme coefficient problems are also solved.

Original languageEnglish
Pages (from-to)1049-1059
Number of pages11
JournalIndian Journal of Pure and Applied Mathematics
Volume29
Issue number10
Publication statusPublished - Oct 1998
Externally publishedYes

Fingerprint

Starlike Functions
Subordination
Unit Disk
Convex function
Extremes
Imply
Subset
Coefficient
Set theory
Theorem
Class
Form

Keywords

  • α-logarithm
  • Convex functions
  • Extreme coefficient problem
  • Fekete-Szegö functional

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

α-Logarithmically convex functions. / Darus, Maslina; Thomas, D. K.

In: Indian Journal of Pure and Applied Mathematics, Vol. 29, No. 10, 10.1998, p. 1049-1059.

Research output: Contribution to journalArticle

Darus, Maslina ; Thomas, D. K. / α-Logarithmically convex functions. In: Indian Journal of Pure and Applied Mathematics. 1998 ; Vol. 29, No. 10. pp. 1049-1059.
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