Subordination properties for meromorphic multivalent functions associated with the multiplier transformation

Panigrahi²,

Mathematical and Computer Modelling

2013

a b s t r a c tIn this paper subordination and inclusion relations are studied for some subclasses of multivalent meromorphic functions in the punctured unit disc having a pole of order p at the origin. The subclasses under investigation are defined through combinations and iterations of a meromorphic analogue of the Cho-Kwon-Srivastava operator for normalized analytic functions. Specially, emphasis is given in this study on the effect of the increase of different parameters on the size of the subclasses. Applications are indicated for the subordination results to electromagnetic cloaking.

Section: Introduction and Definitionsmentioning

confidence: 97%

Subordination and inclusion theorems for subclasses of meromorphic functions with applications to electromagnetic cloaking

Panigrahi²,

Mathematical and Computer Modelling

2013

“…We can observe from Eqs. ( 12) and ( 13), that the admissibility condition for𝜒 as statedin Definition (5), with 𝑛 = 3, is identical to the admissibility for 𝜙 in Definition ( 6 Theorem (9): Let 𝔥 be analytic function in 𝕌, and let ϕ: ℂ 5 × 𝕌 ̅ → ℂ and 𝜒 be given by Eq. ( 14).…”

Section: Results Of Fourth-ordermentioning

confidence: 99%

“…The admissibility for 𝜙 ∈ M 𝑖,1 [Ω, 𝔮], as stated in Definition (6), is comparable to the admissibility requirement for𝜒 as stated in Definition (5), with n=3, as can be seen from Eqs. (29) and (30).…”

Section: 𝔮(𝓏) ≺ 𝓏 −1 ℐ (𝛼𝛽) 𝑓(𝓏)mentioning

confidence: 86%

“…In recent times, for example, a number of authors [3][4][5][6][7][8][9][10][11][12][13][14][15] have developed and talked about the idea of superordination and second-order differential subordination. In addition, a number of writers covered topics such as the theory of thirdorder differential subordination and superordination [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Results of Fourth-Order Differential Superordination and Subordination for Univalent Functions Defined by Integral Operator

Darweesh,

Hasan,

Kadham

2024

MMEP

Exploring some characteristics of differential subordination and superordination of analytic univalent functions in an open unit disc is the aim of this work and additionally, we have the form's normalized Taylor-Maclaurin series:. It also aims to clarify the results of the sandwich. By utilizing the integral operator's properties to examine forth-order differential subordination and superordination of analytic univalent functions, some fascinating results are found and explore forth-order subordinations and superordinations in respect to the convolution. Ultimately, we acquired multiple outcomes concerning fourth-order sandwich theorems inside the open unit disk.

“…a,c) f (z) ν+η 0 (z ∈ U) andνz p m λ+1,p (a,c) f (z)+ηz p m λ,p (a,c) f (z) ν+η µ ∈ H[1, 1] ∩ Q.Let the function ∆(z) be defined on U as in(18). Ifq 1 (z) + zq 1 (z) q 1 (z) ≺ ∆(z) ≺ q 2 (z) + zq 2 λ+1,p (a, c) f (z) + ηz p m λ,p (a,c) f (z) and q 2 are respectively the best subordinant and the best dominant in (29).…”

mentioning

confidence: 99%

Sandwich results for subclasses of multivalent meromorphic functions associated with iterations of the Cho-Kwon-Srivastava transform

Mishra¹,

Soren²

2019

Filomat

In this paper we obtain subordination, superordination and sandwich results for multivalent meromorphic functions, involving the iterations of the Cho-Kwon-Srivastava operator and its combinations. Certain interesting particular cases are also pointed out. ∞ k=1 a k−p z k−p (p ∈ N := {1, 2, 3,. .. }) (2) which are analytic in the punctured unit disc U := U \ {0}. Suppose that f and F are analytic in H. We say that f is subordinate to F, (or F is superordinate to f), write as f ≺ F in U or f (z) ≺ F(z)