Saravanan Gunasekar

Amrita Vishwa Vidyapeetham | AMRITA · Department of Mathematics (Engineering)

The class of Sakaguchi type functions defined by balancing polynomials has been introduced as a novel subclass of bi-univalent functions. The bounds for the Fekete-Szegö inequality and the initial coefficients |a 2 | and |a 3 | have also been estimated.

In this paper, a new subclass, SC µ,p,q σ (r, s; x), of Sakaguchi-type analytic bi-univalent functions defined by (p, q)-derivative operator using Horadam polynomials is constructed and investigated. The initial coefficient bounds for |a 2 | and |a 3 | are obtained. Fekete-Szegö inequalities for the class are found. Finally, we give some corollarie...

The purpose of this research is to unify and extend the study of the well-known concept of coefficient estimates for some subclasses of analytic functions. We define the new subclass A4r,s of analytic functions related to the four-leaf domain, to increase the adaptability of our investigation. The initial findings are the bound estimates for the co...

In this study, we introduce and investigate a novel subclass of analytic bi-univalent functions, which we define using Gegenbauer polynomials. We derive the initial * Corresponding Author. coefficient bounds for |a2|, |a3|, and |a4|, and establish Fekete-Szegö inequalities for this class. In addition, we confirm that Brannan and Clunie's conjecture...

In this paper, a newsubclass of bi-univalent functions using (p,q) −Chebyshev polynomials was constructed by the authors. Initially, the bounds for the first two coefficients viz., |a2|, |a3| were obtained. Finally, Fekete-Szegö inequalitywas calculated.

An introduction of a new subclass of bi-univalent functions involving Sakaguchi type functions defined by(p, q)-fractional operators using Laguerre polynomials have been obtained. Further, the bounds for initial coefficients |a 2 |, |a 3 | and Fekete Szegö inequality have been estimated.

In this research contribution, we have constructed a subclass of analytic bi-univalent functions using Horadam polynomials. Bounds for certain coefficients and Fekete- Szegö inequalities have been estimated.

The authors have introduced a new subclass of bi-univalent functions consisting of Sakaguchi type functions involving \((\mathfrak {p},\mathfrak {q})\)-derivative operator. Further, the estimation of bounds for \(|a_2|\) and \(|a_3|\) has been obtained. The authors have stated a few examples in this paper.KeywordsAnalytic functionBi-univalent funct...

In this research contribution we have considered two subclasses of bi-univalent functions defined using subordination and studied about the bounds for the pre-Schwarzian norm. Initially Shalini et al. have handled this problem. We have made a remark on the proofs and bounds by Shalini et al.

We have constructed a subclass of analytic bi-univalent functions using (\({{\mathfrak {p}}}\),\({{\mathfrak {q}}}\))-Lucas polynomials in this research contribution. Bounds for certain coefficients and Fekete–Szegö inequalities have been estimated.

In this paper, we introduce and investigate a new subclass Q^{∗∗}_{Σ }(α, ϕ) of normalized analytic functions defined using convolution in the open unit disk U whose inverse has univalent analytic continuation to U. Estimates of the coefficients of biunivalent functions belonging to this class are determined by using Faber polynomial techniques.

In this article, two new sub classes of bi-univalent functions have been introduced. The classes have been defined, using Symmetric Q-Derivative Operator and the bounds for functions belonging to these classes have been obtained by using Faber Polynomial Techniques.

In this article we have introduced a class R ~ (η, q, ς), η∈ ℂ− { 0 } of bi-univalent functions defined by symmetric q-derivative operator. We have estimated the upper bounds for the initial coefficients and Fekete-Szeg ö inequality by making use of Chebyshev polynomials.

The objective of the present article is to obtain some constraints that are sufficient for the generalized Struve functions of first kind to belong to the subclasses S*(...), R(...) and to study the inclusion properties.

In this article we have defined a subclass of Bi-univalent functions using symmetric q- derivative operator and estimated the bounds for the coefficients using Faber polynomial techniques. We also have obtained the bounds for the linear functional which is popularly known as Fekete- Szegὅ problem

In this article, we obtain estimates for the coefficients of bi-univalent functions belonging to the class QΣ∗∗ (α), 0 ≤ α < 1 by using Faber polynomial techniques.