Univalent Functions by Means of Chebyshev Polynomials

Abstract

The primary motivation of the paper is to define a new class C h δ α , β , γ which consists of univalent functions associated with Chebyshev polynomials. For this class, we determine the coefficient bound and convolution preserving property. Furthermore, by using subordination structure, two new subclasses of C h δ α , β , γ are introduced and denoted by M λ 1 , λ 2 , s and N λ 1 , λ 2 , s , respectively. For these subclasses, we obtain coefficient estimate, extreme points, integral representation, convexity, geometric interpretation, and inclusion results. Moreover, we prove that, under some restrictions on parameters, C h δ α , β , γ = N λ 1 , λ 2 , s .

The Extension of Chebyshev Polynomial Bounds Involving Bazilevic Function

“…The classical Chebyshev polynomials which are used in this paper, have been in the late eighteenth century, when was defined using de Moivre's formula by Chebyshev(refer (9) ). Such polynomials as (for example) the Fibonacci polynomials, the Lucas polynomials, the Pell polynomials and the families of orthogonal polynomials and other special polynomials as well as their generalizations are potentially important in the fields of probability, statistics, mechanics and number theory (10)(11)(12)(13)(14) 2 Methodology…”

Subclasses of Analytic Functions with Negative Coefficients Involving q-Derivative Operator

“…For f ∈ V , there are some signi cant researchers for example in (Halim et al, 2005) , the authors studied the class M * S V (𝜂 , 𝜗) consisting of starlike functions with respect to (w.r.t) symmetric points. Besides, there are various studies for example in (Al-Abbadi and Darus, 2010;Al Shaqsi and Darus, 2007;Atshan and Ghawi, 2012;Bucur and Breaz, 2020;Choo and Janteng, 2013;Halim et al, 2006;Janteng and Halim, 2009;Najafzadeh and Salleh, 2022;Oluwayemi et al, 2022;Porwal et al, 2022).…”