Abstract
One of the classical problems concerns the class of analytic functions f on the open unit disk |z| < 1 which have finite Dirichlet integral Δ(1, f), where
The class \({\mathcal{S} ^*(A,B)}\) of normalized functions f analytic in |z| < 1 and satisfies the subordination condition \({zf'(z)/f(z)\prec (1+Az)/(1+Bz)}\) in |z| < 1 and for some \({-1\leq B\leq 0}\) , \({A \in \mathbb{C}}\) with \({A\neq B}\) , has been studied extensively. In this paper, we solve the extremal problem of determining the value of
as a function of r. This settles the question raised by Ponnusamy and Wirths (Ann Acad Sci Fenn Ser AI Math 39:721–731, 2014). One of the particular cases includes solution to a conjecture of Yamashita which was settled recently by Obradović et al. (Comput Methods Funct Theory 13:479–492, 2013).
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S. Ponnusamy is on leave from the Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India.
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Ponnusamy, S., Sahoo, S.K. & Sharma, N.L. Maximal Area Integral Problem for Certain Class of Univalent Analytic Functions. Mediterr. J. Math. 13, 607–623 (2016). https://doi.org/10.1007/s00009-015-0521-7
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DOI: https://doi.org/10.1007/s00009-015-0521-7