Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces

Author:

Zhang Ruyu1,Ouyang Dongling1,Xiong Liangpeng1

Affiliation:

1. School of Mathematics and Computer Science, Jiangxi Science and Technology Normal University , Nanchang , Jiangxi , CHINA

Abstract

ABSTRACT In this paper, the sharp solutions of Fekete-Szegö problems are provided for class of quasi-convex mappings f 1 of type B and class of quasi-convex mappings f 2 of type B and order α defined on the unit ball in a complex Banach space, respectively, where x = 0 is a zero of order k + 1 of fi (x) − x (i = 1, 2). Compare with some recent works, our main theorems hold without additional restrictive conditions. Also, the proof of our main theorems are more simple than those given in the previous results.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference21 articles.

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2. Cartan, H.: Sur la possibilité détendre aux fonctions de plusieurs variables complexes la théorie des fonctions univalentes. In: Lecons sur les Fonctions Univalentes ou Multivalentes (P. Montel, ed.), Gauthier-Villars, Paris, 1933.

3. De Branges, L.: A proof of the Bieberbach conjecture, Acta. Math. 154 (1985), 137–152.

4. Dlugosz, R.—Liczberski, P.: Some results of Fekete-Szegö type for Bavrin’s families of holomorphic functions in ℂn , Ann. Mat. Pura Appl. 200 (2021), 1841–1857.

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