• Corpus ID: 252439160

On the generalized Zalcman conjecture for the class of univalent functions using variational method

  title={On the generalized Zalcman conjecture for the class of univalent functions using variational method},
  author={Vasudevarao Allu and Abhishek Pandey},
. Let S denote the class of analytic and univalent ( i.e. , one-to-one) functions f ( z ) = z + P ∞ n =2 a n z n in the unit disk D = { z ∈ C : | z | < 1 } . For f ∈ S , In 1999, Ma proposed the generalized Zalcman conjecture that | a n a m − a n + m − 1 | ≤ ( n − 1)( m − 1) , for n ≥ 2 , m ≥ 2 , with equality only for the Koebe function k ( z ) = z/ (1 − z ) 2 and its rotations. In the same paper, Ma [19] asked for what positive values of λ does the following inequality hold? 3) . Clearly… 



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UNIVALENT FUNCTIONS (Grundlehren der mathematischen Wissenschaften, 259)