Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON PARTIAL SOLUTIONS TO CONJECTURES FOR RADIUS PROBLEMS INVOLVING LEMNISCATE OF BERNOULLI

  • Gurpreet Kaur (Department of Mathematics, Mata Sundri College for Women, University of Delhi)
  • Received : 2023.08.07
  • Accepted : 2023.11.07
  • Published : 2023.12.30
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Abstract

Given a function f analytic in open disk centred at origin of radius unity and satisfying the condition |f(z)/g(z) - 1| < 1 for a analytic function g with certain prescribed conditions in the unit disk, radii constants R are determined for the values of Rzf'(Rz)/f(Rz) to lie inside the domain enclosed by the curve |w2 - 1| = 1 (lemniscate of Bernoulli). This, in turn, provides a partial solution to the conjectures and problems for determination of sharp bounds R for such functions f.

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References

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