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In this paper, we aim to give some results for third-order differential subordination for analytic functions in the open unit disk U = z : z ∈ C   a n d   z < 1 involving the new integral operator μ α , n m (f ∗ g) . The results are obtained by examining pertinent classes of acceptable functions. New findings on differential subordination have been obtained. Additionally, some specific cases are documented. This work investigates appropriate classes of admissible functions, presents a novel of new integral operator, and discusses the properties of third-order differential subordination. The properties and results of the differential subordination are symmetrical to the properties of the differential superordination to form the sandwich theorems. [ABSTRACT FROM AUTHOR]

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Using the results of 3rd order differential subordination, we introduce certain families of admissible functions and discuss some applications of 3rd order differential subordination for normalized analytic functions associated with novel fractional operator namely Zeta-Riemann Fractional differential operator. Some new results on differential subordination and superordination with some sandwich theorems are obtained. Moreover, several particular cases are also noted. [ABSTRACT FROM AUTHOR]

This study introduces two new subclasses Τ...Σ (τ, λ, η, γ; α) and T...Σ (τ, λ, η, γ; β), of the function class Σ. These subclasses are defined in the open unit disc and consist of analytic bi-univalent functions. Moreover, in these newly created subclasses, we get approximations for the coefficients |a2| and |a3| in the functions. Additional findings have been acquired. [ABSTRACT FROM AUTHOR]

In the current work, we investigate two new subclasses G∑(δ,α,τ) and G*∑(δ,α,β) of class ∑ of bi-univalent functions found within the open unit disk U={z: |z| <1}. We derive the normalized forms of functions that belong to the two classes described above. Furthermore, we obtain estimate s of the starting coefficients | | and | |for these functions. Multiple classifications are also taken into consideration, and connections to previously established findings are established. [ABSTRACT FROM AUTHOR]

The present study introduces and examines two specific subclasses, M∑q (β,ρ,λ) and w∑q(τ,μ,η,Φ) of bi-univalent functions that are defined by quasi-subordination. We obtain approximations for the Taylor-Maclaurin coefficients |a2| and |a3| for functions within these subclasses. [ABSTRACT FROM AUTHOR]

The purpose of this study is to establish new subclasses within the function class ∑m, which consists of analytic as well as m-fold symmetric bi-univalent functions expressed within the open unit disk Q. Additionally, for functions belonging to each of the newly established subclasses, this paper establishes estimates with regards to the Taylor-Maclaurin coefficients given by |am+1| as well as |a2m+1| Moreover, we take into consideration of specific as well as existing special cases for our respective findings. [ABSTRACT FROM AUTHOR]

This paper introduces fractional operators in the complex domain as generalizations for the Srivastava–Owa operators. Some properties for the above operators are also provided. We discuss the convexity and starlikeness of the generalized Libera integral operator. A condition for the convexity and starlikeness of the solutions of fractional differential equations is provided. Finally, a fractional differential equation is converted into an ordinary differential equation by wave transformation; illustrative examples are provided to clarify the solution within the complex domain. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain sandwich theorems for univalent functions by using some results of differential subordination and superordination for univalent functions involving integral operator. [ABSTRACT FROM AUTHOR]

In this paper, The property of subordination is used to define the subclass F(δ, z, t), |an| bounds on the coefficients. The upper bound for the functions in this class is provided for n = 2,3,4, 5,6,7. The fourth Hankel determinant for a class F(δ, z, t) is obtained. Some new results also are obtained. [ABSTRACT FROM AUTHOR]

In this article, we aim to describe a new operator J(s,a,μ)(δ,λ) via convolution. Moreover, we aim to present a new subclass CΣm (τ;β) related to m-fold symmetric bi-univalent functions in the open unit disk Θ={z∈C∶|z| ˂ 1 }. Finally, an estimate related to the Hankel determinant for functions in CΣm (τ;β) are given. [ABSTRACT FROM AUTHOR]

In this research paper, we explain the use of the convexity and the starlikness properties of a given function to generate special properties of differential subordination and superordination functions in the classes of analytic functions that have the form f (z) = z + ∑n=2∞; anzn in the unit disk. We also show the significant of these properties to derive sandwich results when the Srivastava- Attiya operator Fσ,bf(z) is used. [ABSTRACT FROM AUTHOR]

Making use of Gegenbauer polynomials, we initiate and explore two sets of normalized regular and bi-univalent (or bi-Schlicht) functions in D = |z 2 C: |z| < 1g linked with Gegenbauer polynomials. We investigate certain coefficients bounds and the Fekete-Szegö functional for functions in these families. We also present few interesting observations and provide relevant connections of the results investigated. [ABSTRACT FROM AUTHOR]