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Fekete–Szegö problem for some starlike functions related to shell-like curves

  • Ravinder Krishna Raina EMAIL logo and Janusz Sokół
Published/Copyright: April 28, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

In this note, we investigate the Fekete-Szegö problem for a class 𝓢𝒽 of functions f analytic in the open unit disc Δ = {z: |z| < 1} (and which is related to a shell-like curve associated with Fibonacci numbers) satisfying the conditions that

f(0)=0,  f′(0)=1  and  zf′(z)f(z)≺1+τ2z21−τz−τ2z2 (z∈Δ),

where ≺ denotes the subordination and the number τ=(1−5)/2 is such that |τ| fulfils the golden section of the segment [0,1].

Keywords: univalent functions; convex functions; starlike functions; subordination; Fibonacci numbers; conchoid of de Sluze; trisectrix of Maclaurin
MSC: Primary 30C45; Secondary 30C80
Present address: 10/11 Ganpati Vihar Opposite Sector 5 Udaipur 313002 INDIA

  1. This paper has been communicated by Ján Borsík

References

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Received: 2012-12-6
Accepted: 2013-4-22
Published Online: 2016-4-28
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0123
Keywords for this article
univalent functions; convex functions; starlike functions; subordination; Fibonacci numbers; conchoid of de Sluze; trisectrix of Maclaurin

Articles in the same Issue

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  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
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  9. Research Article
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  11. Research Article
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  13. Research Article
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