Maximal Area Integral Problem for Certain Class of Univalent Analytic Functions

Authors

Saminathan Ponnusamy, Indian Statistical Institute Chennai
Swadesh Kumar Sahoo, Indian Institute of Technology Indore
Navneet Lal Sharma, Indian Institute of Technology Indore

Article Type

Research Article

Publication Title

Mediterranean Journal of Mathematics

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 (Formula presented.). The class (Formula presented.) of normalized functions f analytic in |z| < 1 and satisfies the subordination condition (Formula presented.) in |z| < 1 and for some (Formula presented.), (Formula presented.) with (Formula presented.), has been studied extensively. In this paper, we solve the extremal problem of determining the value of (Formula presented.) 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).

First Page

607

Last Page

623

DOI

10.1007/s00009-015-0521-7

Publication Date

4-1-2016

Comments

Open Access; Green Open Access

Recommended Citation

Ponnusamy, Saminathan; Sahoo, Swadesh Kumar; and Sharma, Navneet Lal, "Maximal Area Integral Problem for Certain Class of Univalent Analytic Functions" (2016). Journal Articles. 4291.
https://digitalcommons.isical.ac.in/journal-articles/4291