On a subclass of certain convex functions with negative coefficients

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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“…The class S n (γ, λ, β) was studied by [15]. Since A is class of functions f (z) of the form f (z) = …”

Section: Definition 11 (N δ)-Neighborhood·mentioning

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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“…In our investigation of the inclusion relations involving N n,δ (e), we shall require the following Lemma which was proved in [3].…”

Section: A Set Of Inclusion Relations Involvingmentioning

confidence: 99%

“…and for all z ∈ U [3]. We note that C(1, 0, α) ≡ C(α) is the generalization of C(α) by H.Silverman [4].…”

Section: Introductionmentioning

confidence: 96%

Neighborhoods of a class of analytic functions with negative coefficients

Guney¹,

Eker²

2006

imf

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“…We note that (i) G p n (α, β, 0, 0, γ, δ) was introduced by Xiao-Fei and An-Ping [9]; (ii) G 1 n (α, β, 0, 0, γ, δ) was introduced by Kamali and Akbulut [10].…”

Section: Introductionmentioning

confidence: 99%

Fractional Derivative Operator for P-Valent Functions With Negative Coefficients

2018

Acta Univ. Apulensis Math. Inform.

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In this paper, a differential operator D m p,µ,λ,σ (α, β)f (z) defined in the open unit disc U = {z ∈ C : |z| < 1} is introduced. By using this operator, we introduce a new subclass of analytic functions G p n (α, β, µ, λ, γ, δ). Moreover, we discuss coefficient inequality, Hadamand product, growth and distortion theorems, closure theorems, radii of close-to-convexity, starlikeness, convexity and integral operators. Furthermore, we give an application involving fractional calculus for functions in G p n (α, β, µ, λ, γ, δ).

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On a subclass of certain convex functions with negative coefficients

Cited by 16 publications

References 1 publication

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

Neighborhoods of a class of analytic functions with negative coefficients

Fractional Derivative Operator for P-Valent Functions With Negative Coefficients

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