Neighborhoods of certain analytic 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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“…Similar work has been seen for different subclasses done by other authors (see for example [17,18,19].…”

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

confidence: 88%

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

Darus

Faisal

2012

Tamkang J. Math.

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“…were extensively studied by Altıntaş and Owa [15] and certain conditions for hypergeometric functions and generalized Bessel functions for these classes were studied by Moustafa [16] and by Porwal and Dixit [17]. …”

Section: Tc mentioning

confidence: 99%

Characteristic Properties of the New Subclasses of Analytic Functions

Mustafa¹

2017

deufmd

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“…Following the earlier investigations by Goodman [11], Ruscheweyh [22] and others including Altintas and Owa [4], Altintas et al ([5] and [6]), we first define the (n, δ)-neighborhood of a function f ∈ A p (n), given by (1.1) as follows:…”

Section: Inclusion Relationships Involving Neighborhoodsmentioning

confidence: 99%

INCLUSION AND NEIGHBORHOOD PROPERTIES OF CERTAIN SUBCLASSES OF p-VALENT ANALYTIC FUNCTIONS OF COMPLEX ORDER INVOLVING A LINEAR OPERATOR

Sahoo¹,

Patel²

2014

Bulletin of the Korean Mathematical Society

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Abstract. By making use of the familiar concept of neighborhoods of analytic functions, we prove several inclusion relationships associated with the (n, δ)-neighborhoods of certain subclasses of p-valent analytic functions of complex order with missing coefficients, which are introduced here by means of the Saitoh operator. Special cases of some of the results obtained here are shown to yield known results.

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Neighborhoods of certain analytic functions with negative coefficients

Abstract: The object of the present paper is to derive some properties of neighborhoods of analytic functions with negative coefficients in the open unit disk

Cited by 74 publications

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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

Characteristic Properties of the New Subclasses of Analytic Functions

INCLUSION AND NEIGHBORHOOD PROPERTIES OF CERTAIN SUBCLASSES OF p-VALENT ANALYTIC FUNCTIONS OF COMPLEX ORDER INVOLVING A LINEAR OPERATOR

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