Main differential sandwich theorem with some applications

Al-Refai, Oqlah; Darus, Maslina

doi:10.1134/s1995080209010016

Cited by 8 publications

(4 citation statements)

References 10 publications

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“…Remark 2.1. Other work associated with the derivative and integral operator for different issues can be determined in [2,3,12] and [19].…”

Section: Proof Define the Functionmentioning

confidence: 99%

Differential Subordination and Superordination for a Generalized Differential Operator Involving Mittag-Leffler Function

ELHADDAD¹,

DARUS²

2021

KgJMat

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Abstract. Owning to the importance and great interest of linear operators, a generalisation of linear derivative operator He m δ,p(α, β, a1, b1)f(z) is newly introduced in this study. The main objective of this paper is to investigate various subordination and superordination related to the aforementioned generalised linear derivative operator. Additionally, the resultant sandwich-type of this operator is also considered.

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“…Remark 2.1. Other work associated with the derivative and integral operator for different issues can be determined in [2,3,12] and [19].…”

Section: Proof Define the Functionmentioning

confidence: 99%

Differential Subordination and Superordination for a Generalized Differential Operator Involving Mittag-Leffler Function

ELHADDAD¹,

DARUS²

2021

KgJMat

Self Cite

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“…Proof. (a) Since it is given that f (z) = z − ∞ k=n a k+1 z k+1 ∈ S n,µ (γ, α, β, λ, ℧,ω), this implies that ∞ k=n (1 + kλω α ) ℧+1 (1 + µkλω α )(k + 1)(β|γ| + kλω α )a k+1 ≤ β|γ|, similarly g (z) = z − ∞ k=n b k+1 z k+1 ∈ R n,µ (γ, α, β, λ, ℧,ω) implies Other work regarding differential operators for various problems can be found in ( [11], [24]- [28], [20], [14], [13]).…”

Section: Hadamard Productmentioning

confidence: 99%

Some subclasses of analytic functions of complex order defined by new differential operator

Darus

Faisal

2012

Tamkang J. Math.

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Let \hskip 2pt $\mathcal{A}(n)$ \hskip 2pt denote \hskip 2pt the \hskip 2pt class \hskip 2pt of \hskip 2pt analytic \hskip 2pt functions \hskip 2pt $f$ \hskip 2pt in \hskip 2pt the \hskip 2pt open \hskip 2pt unit \hskip 2pt disk \hskip 2pt $U=\{z:|z|<1\}$ \hskip 2pt normalized \hskip 2pt by \hskip 2pt $f(0)=f'(0)-1=0.$ \hskip 2pt In \hskip 2pt this \hskip 2pt paper, \hskip 2pt we \hskip 2pt introduce \hskip 2pt and \hskip 2pt study \hskip 2pt the \hskip 2pt classes \hskip 2pt $S_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho)$ \hskip 2pt and \hskip 2pt $R_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho)$ \hskip 2pt of \hskip 2pt functions \hskip 2pt $f\in\mathcal{A}(n)$ with $(\mu)z(D^{\mho+2}_{\lambda}(\alpha, \omega)f(z))'+(1-\mu)z(D^{\mho+1}_{\lambda}(\alpha, \omega)f(z))'\neq0$ and satisfy some conditions available in literature, where $f\in\mathcal{A}(n), \alpha, \omega, \lambda, \mu \geq0, \mho\in \mathbb{N}\cup\{0\},\,\,z\in U,$ and $D^{m}_{\lambda}(\alpha, \omega)f(z): \mathcal{A}\rightarrow \mathcal{A},$ is the linear fractional differential operator, newly defined as follows $$D^{m}_{\lambda}(\alpha, \omega)f(z) = z+ \sum\limits_{k=2}^{\infty}a_{k}(1+(k-1)\lambda \omega^{\alpha})^{m}z^{k}\cdot$$ Several properties such as coefficient estimates, growth and distortion theorems, extreme points, integral means inequalities and inclusion for the functions included in the classes $S_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho, \omega)$ and $R_{n, \mu}(\gamma, \alpha, \beta, \lambda, \mho, \omega)$ are given.

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“…Other work regarding differential operators for various problems can be found in ( [11], [24]- [28], [20], [14], [13]). …”

Section: Hadamard Productmentioning

confidence: 99%

Some subclasses of analytic functions of complex order defined by new differential operator

Darus

Faisal

2012

Tamkang J. Math.

Self Cite

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Abstract. Let A (n) denote the class of analytic functions f in the open unit disk U = {z : |z| < 1} normalized by f (0) = f ′ (0) − 1 = 0. In this paper, we introduce and study the classes S n,µ (γ, α, β, λ, ℧) andand satisfy some conditions avail- is the linear fractional differential operator, newly defined as followsSeveral properties such as coefficient estimates, growth and distortion theorems, extreme points, integral means inequalities and inclusion for the functions included in the classes S n,µ (γ, α, β, λ, ℧,ω) and R n,µ (γ, α, β, λ, ℧,ω) are given.

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Main differential sandwich theorem with some applications

Cited by 8 publications

References 10 publications

Differential Subordination and Superordination for a Generalized Differential Operator Involving Mittag-Leffler Function

Differential Subordination and Superordination for a Generalized Differential Operator Involving Mittag-Leffler Function

Some subclasses of analytic functions of complex order defined by new differential operator

Some subclasses of analytic functions of complex order defined by new differential operator

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