Article ID: MTJPAM-D-24-00214

Title: Functional properties for a class of analytic functions associated with the four-leaf domain


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00214; Volume 7 / Issue 4 / Year 2025, Pages 30-47

Document Type: Research Paper

Author(s): Eureka Pattnayak a , Trailokya Panigrahi b

aInstitute of Mathematics and Applications, Andharua, Bhubaneswar-751029, Odisha, India

bInstitute of Mathematics and Applications, Andharua, Bhubaneswar-751029, Odisha, India

Received: 9 December 2024, Accepted: 4 January 2026, Published: 13 April 2026

Corresponding Author: Trailokya Panigrahi (Email address: trailokya.ima@iomaorissa.ac.in)

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Abstract

By making use of subordination between two analytic functions, the authors introduce a novel subclass of analytic functions related to four-leaf domain defined in the domain of open unit disk. This subclass is related to those defined by Ma and Minda [14] in 1992. We determine the upper bounds on the initial four coefficients of the function belongs to this new class and of the Fekete-Szegö functional and Hankel determinants of various orders. We prove that the Zalcman conjecture holds true for the class if n = 3. Further, we investigate the upper bounds of Vandermonde and Toeplitz determinant of different orders. The estimate on modular difference of two successive coefficient of the function for the said class is determined. The method we used consisting of two recent inequalities that are related to the first three coefficients and the inequality between arbitrary coefficients for carathéodory function due to Ravichandran and Verma.

Keywords: Analytic function, subordination, Hankel determinants, Toeplitz determinants, Vandermonde determinants, module difference, Krushkal inequality, Zalcman functional

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Cite this article

How to cite this article: E. Pattnayak and T. Panigrahi, Functional properties for a class of analytic functions associated with the four-leaf domain, Montes Taurus J. Pure Appl. Math. 7 (4), 30-47, 2025; Article ID: MTJPAM-D-24-00214.