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In this paper, we introduce and investigate a new family, denoted by 𝒲Σsc (λ, η, δ, r), of normalized holomorphic and bi-univalent functions with respect to symmetric conjugate points, defined in 𝕌, by making use the Borel distribution series, which is associated with the Horadam polynomials. We derive estimates on the initial Taylor-Maclaurin coefficients and solve the Fekete-Szeg˝o type inequalities for functions in this family.

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In present manuscript, we introduce and study two families BS(l, d; a) and B * S (l, d; b) of holomorphic and bi-univalent functions which involve the Borel distribution series. We establish upper bounds for the initial Taylor-Maclaurin coefficients |a2| and |a3| for functions in each of these families. We also point out special cases and consequences of our results.

In the present article, we determine some subordination and superordination results involving Wanas operator for certain normalized analytic functions defined in the unit disk U. These results are applied to establish sandwich results. Our results extend corresponding previously known results.

The main object of the present paper is to use Mittag-Leffler function to introduce and study two new classes RSm(g, l, e, d, t ; a) and R * Sm(g, l, e, d, t ; b) of Sm consisting of analytic and m-fold symmetric bi-univalent functions defined in the open unit disk U. Also, we determine the estimates on the initial coefficients |am+1| and |a2m+1| for functions in each of these new classes. Furthermore, we indicate certain special cases for our results.

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey's fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters. [ABSTRACT FROM AUTHOR]

In the present paper, we define and study a new family of holomorphic functions which involve the Bazilevič functions and the λ -pseudo-starlike functions. We establish coefficient estimates for the first four determinants of the symmetric Toeplitz matrices T 2 (2) , T 2 (3) , T 3 (1) and T 3 (2) for the functions in this family. Further, we investigate several special cases and consequences of our results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a linear operator and define a certain class Ep(a, c, λ, γ: h) of analytic and multivalent functions in the open unit disk associated with differential subordination. Also, we discuss some geometric properties for this class. [ABSTRACT FROM AUTHOR]

Our paper introduces a new linear operator using the convolution between a Mittag Leffler Function and basic hypergeometric function. Use of the linear operator creates a new class of meromorphic functions defined in the punctured open unit disk. Consequently, the paper examines different aspects Apps and assets like, extreme points, coefficient inequality, growth and distortion. In conclusion, the work discusses modified Hadamard product and closure theorems. [ABSTRACT FROM AUTHOR]

The aim of this work is to introduce two families, BΣ(P;ϑ) and OΣ(X;ϑ), of holomorphic and bi-univalent functions involving the Bazilevič functions and the Ozaki-close-to-convex functions, by using generalized telephone numbers. We determinate upper bounds on the Fekete-Szegö type inequalities and the initial Taylor-Maclaurin coefficients for functions in these families. We also highlight certain edge cases and implications for our findings. [ABSTRACT FROM AUTHOR]

In this study, we introduce a new class of normalized analytic and bi-univalent functions denoted by D Σ (δ , η , λ , t , r) . These functions are connected to the Bazilevič functions and the λ -pseudo-starlike functions. We employ Sakaguchi Type Functions and Horadam polynomials in our survey. We establish the Fekete-Szegö inequality for the functions in D Σ (δ , η , λ , t , r) and derive upper bounds for the initial Taylor–Maclaurin coefficients | a 2 | and | a 3 | . Additionally, we establish connections between our results and previous research papers on this topic. [ABSTRACT FROM AUTHOR]

In the present article, we introduce two families ΒΣ(δ,α,λ,m,n,t) and FΣ(δ,λ,γ,m,n,t) of holomorphic and bi-univalent functions associating λ-pseudo-starlike and convex functions with Sakaguchi type functions defined by Gegenbauer polynomials. We derive the initial Maclaurin coefficients estimates and determinate the Fekete-Szegö problem of functions in these families. [ABSTRACT FROM AUTHOR]

In this paper we establish upper bounds for the second and third coefficients of holomorphic and bi-univalent functions in a new family which involve the Bazilevič functions and β-pseudo-starlike functions under a new operator joining Poisson distribution with Ruscheweyh derivative operator. Also, we discuss Fekete-Szegö problem of functions in this family. [ABSTRACT FROM AUTHOR]

The objective of this research is to produce robust differential subordination and differential superordination results using the fractional integral of the Wanas differential operator. These results apply to Analytic functions defined on U ×Ū, with Coefficient functions that are holomorphic in U. Furthermore, for each instance of strong differential subordination and strong differential superordination, we provide the most superior dominant and the most subordinate subordinant. These findings are used to achieve strong sandwich results. [ABSTRACT FROM AUTHOR]

One of the important problems regarding coefficients of analytical functions (i.e., Fekete–Szegö inequality) was raised by Fekete and Szegö in 1933. The results of this research are dedicated to determine upper coefficient estimates and the Fekete–Szegö problem in the class W Σ (δ , λ ; ϑ) , which is defined by generalized telephone numbers. We also indicate some specific conditions and consequences of results found by us. [ABSTRACT FROM AUTHOR]