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Title: | SOME COEFFICIENT PROBLEMS FOR A CLASS OF STARLIKE FUNCTIONS |
Authors: | YADAV, VISHAL RAJ |
Keywords: | COEFFICIENT PROBLEMS STARLIKE FUNCTIONS GEOMETRIC FUNCTION THEORY DETERMINANTS COEFFICIENTS |
Issue Date: | May-2025 |
Series/Report no.: | TD-7915; |
Abstract: | This investigation explores the analytic and geometric properties of complex func tions. Specifically, we focus on a novel starlike function that is analytic, denoted as S ∗ nc, which is uniquely associated with a non-convex domain. The class on which we are going to work is defined as : S ∗ nc = f ∈ A : z f ′ (z) f(z) = 1 + z cos z ≺ φnc(z), z ∈ D . Here, A represents the set of functions analytic in D that satisfy f(0) = 0 and f ′ (0) = 1. The subordination condition involves a specific non-convex function φnc(z) = (1 + z)/cos z, which characterizes the geometric properties of functions belonging to this class. Our primary objective is to determine the sharp second-order of Hankel and Toeplitz determinats for the logarithmic coefficients of functions f belonging to this newly de fined class S ∗ nc. Furthermore, the study extends to finding these precise bounds for the logarithmic coefficients of z their inverse functions, f −1 . The determination of sharp bounds for these determinants and coefficients provides crucial insights into the in tricate behavior and structural properties of these analytic functions within the speci fied non-convex domain, contributing significantly to the understanding of coefficient problems in geometric function theory. |
URI: | http://dspace.dtu.ac.in:8080/jspui/handle/repository/21678 |
Appears in Collections: | M Sc Applied Maths |
Files in This Item:
File | Description | Size | Format | |
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Vishal Raj Yadav M.Sc..pdf | 1.03 MB | Adobe PDF | View/Open |
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