The Extension of Chebyshev Polynomial Bounds Involving Bazilevic Function

S Chinthamani; P Lokesh

doi:10.17485/IJST/v16i27.icrms-207

Article

The Extension of Chebyshev Polynomial Bounds Involving Bazilevic Function

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i27.icrms-207

Year: 2023, Volume: 16, Issue: 27, Pages: 2040-2046

Original Article

The Extension of Chebyshev Polynomial Bounds Involving Bazilevic Function

S Chinthamani^1*, P Lokesh²

¹Department of Mathematics, Stella Maris College, Cathedral Road, Tamil Nadu, India
²Department of Mathematics, Adhiparasakthi College of Engineering, Kalavai, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:26 May 2023, Accepted Date:01 June 2023, Published Date:18 July 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: To propose a new class of bi-univalent function based on Bazilevic Sakaguchi function using the trigonometric polynomials Tn ( q;eiq ) and to find the Taylor – Maclaurin coefficient inequalities and Fekete – Szego inequality for upper bounds. Methods: The Chebychev’s polynomial has vast applications in GFT. The powerful tool called convolution (Or Hadamard product), subordination techniques are used in designing the new class. In establishing the core results, derivative tests, triangle inequality and appropriate results that are existing are used. Findings:The trigonometric polynomials are applied and a class of Bi-univalent functions Pa;b;c S (l ;t ;q;q ) involving Bazilevic Sakaguchi function is derived. More over, the maximum bounds for initial coefficients and Fekete-Szego functional for the underlying class are computed. This finding opens the door to young researchers to move further with successive coefficient estimates and related research. Novelty:In recent days, several studies on Chebyshev’s polynomial are revolving around univalent function classes among researchers. But in this article a significant amount of interplay between Chebyshev’s polynomial and Bazilevic Sakaguchi function associated with Bi-univalent functions is clearly established.

Keywords: Bistarlike functions; Bi-Starlike Functions; Bi-Univalent Functions; Sakaguchi Type Functions; Subordination; Trigonometric Polynomials

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Copyright

© 2023 Chinthamani & Lokesh. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)