Certain Geometric Properties of Meromorphic Functions Defined by a New Linear Differential Operator

Abstract

In the present paper, we investigate a new linear operator through the Hadamard product between the fundamental hypergeometric function and the Mittag Leffler function. Furthermore, the geometric properties of a new meromorphic function subclass will be investigated.

Some Classes of Univalent Function with Negative Coefficients

“…For this class, we discovered both necessary with sufficient condition in respect of coefficients., and used it to get improved findings for some numbers related to the conformal mapping of univalent functions. For the classes 𝑆 * (𝜏) and 𝐶 * (𝜏), Silverman [13,14] established coefficient inequalities, distrtion, and coveing theorems [4][5][6][7][8]. Sharp coefficients and distrtion theorems are found for the classes 𝑆 * (𝜏, 𝜆) and 𝐶 * (𝜏, 𝜆) in this study.…”

“…Select 𝑤 values on the real axis such that [𝑤ℎ ′ (𝑤) ℎ(𝑤) ⁄ ] is true . We get (7) by clearing the denominator and allowing 𝑤 ⟶ 1 go through real values, we…”

Several Subclasses of r-Fold Symmetric Bi-Univalent Functions possess Coefficient Bounds

“…Furthermore, if the function ℎ is univalent in 𝑈, then we get the following equivalence ℎ(𝑤) ≺ 𝑘(𝑤) is obtained if and only if ℎ(0) = 𝑘(0) and ℎ(𝑈) ⊂ 𝑘(𝑈) , this can be shown in [2][3][4][5][6].…”

Higher-Order Derivatives of Differential Subordination of Multivalent Functions

“…written as ℊ ≺ 𝑘 𝑜𝑟 ℊ(𝑤) ≺ 𝑘(𝑤), (𝑤 ∈ ℒ) Furthermore, if the function k is univalent in ℒ, then we get the following equivalence ℊ(𝑤) ≺ 𝑘(𝑤) if and only if ℊ(0) = 𝑘(0) and ℊ(ℒ) ⊂ 𝑘(ℒ) [20][21][22]. A function ℊ(𝑤) is called starlike (convex) in ℒ if satisfies the following condition:…”