On arclength problem for analytic functions

Let A be the class of functions g ( z ) = z + ∑ n = 2 ∞ a n z n which are analytic in the unit disk D = { z : | z | < 1 } . We denote by C ( r ,  g ) the closed curve which is the image of | z | = r < 1 under the mapping w = g ( z ) , furthermore we denote by L ( r ,  g ) the length of C ( r ,...

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Veröffentlicht in:Analysis and mathematical physics 2023-06, Vol.13 (3), Article 45
Hauptverfasser: Chudziak, Małgorzata, Nunokawa, Mamoru, Sokół, Janusz, Trybucka, Edyta
Format: Artikel
Sprache:eng
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Zusammenfassung:Let A be the class of functions g ( z ) = z + ∑ n = 2 ∞ a n z n which are analytic in the unit disk D = { z : | z | < 1 } . We denote by C ( r ,  g ) the closed curve which is the image of | z | = r < 1 under the mapping w = g ( z ) , furthermore we denote by L ( r ,  g ) the length of C ( r ,  g ). In this paper we are interested in finding the maximum of the length L ( r ,  f ) as f ( z ) runs through all members of a fixed class of functions.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-023-00806-w