scholarly journals Convolution Properties of p-Valent Functions Associated with a Generalization of the Srivastava-Attiya Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Priyabrat Gochhayat
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Fractional Differintegral ◽  
Convolution Properties ◽  
Class Of Functions ◽  
Fractional Differintegral Operator

Let 𝒜p denote the class of functions analytic in the open unit disc 𝕌 and given by the series f(z)=zp+∑n=p+1∞anzn. For f∈𝒜p, the transformation ℐp,δλ:𝒜p→𝒜p defined by ℐp,δλf(z)=zp+∑n=p+1∞((p+δ)/(n+δ))λanzn,  (δ+p∈ℂ∖ℤ0-,  λ∈ℂ;  z∈𝕌), has been recently studied as fractional differintegral operator by Mishra and Gochhayat (2010). In the present paper, we observed that ℐp,δλ can also be viewed as a generalization of the Srivastava-Attiya operator. Convolution preserving properties for a class of multivalent analytic functions involving an adaptation of the popular Srivastava-Attiya transform are investigated.

scholarly journals Convolution Properties for Certain Classes of Analytic Functions Defined byq-Derivative Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
T. M. Seoudy ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Convolution Properties

We investigate convolution properties and coefficients estimates for two classes of analytic functions involving theq-derivative operator defined in the open unit disc. Some of our results improve previously known results.

scholarly journals Convolution Properties of Certain Classes of Analytic Functions Defined by Jackson q-Derivative

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 105
Author(s):  
Abdel Moneim Y. Lashin ◽  
Badriah Maeed Algethami ◽  
Abeer O. Badghaish
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Inclusion Properties ◽  
Convolution Properties

In this paper, the Jackson q-derivative is used to investigate two classes of analytic functions in the open unit disc. The coefficient conditions and inclusion properties of the functions in these classes are established by convolution methods.

scholarly journals Functions starlike with respect to other points

1991 ◽  
Vol 14 (3) ◽  
pp. 451-456 ◽  
Author(s):  
S. Abdul Halim
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Real ◽  
Symmetric Points ◽  
Class Of Functions

In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. Forp≤β<1, letSS*(β)be the class of normalised analytic functionsfdefined in the open unit discDsuch thatRezf′(z)/(f(z)−f(−z))>β, for somez ϵ D. In this paper, we introduce 2 other similar classesSC*(β),SSC*(β)as well as give sharp results for the real part of some function forf ϵ SS*(β),SC*(β)andSSC*(β)The behaviour of certain integral operators are also considered.

Some properties of the analytic functions with bounded radius rotation

2019 ◽  
Vol 28 (1) ◽  
pp. 85-90
Author(s):  
YASAR POLATOGLU ◽  
◽  
ASENA CETINKAYA ◽  
OYA MERT ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Bounded Radius Rotation

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

Coefficient Inequalities for Lp-Valued Analytic Functions

1981 ◽  
Vol 24 (3) ◽  
pp. 347-350
Author(s):  
Lawrence A. Harris
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Inequalities

AbstractA Hausdorff-Young theorem is given for Lp-valued analytic functions on the open unit disc and estimates on such functions and their derivatives are deduced.

scholarly journals Class of Analytic Function Related with Uniformly Convex and Janowski’s Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Akhter Rasheed ◽  
Saqib Hussain ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

scholarly journals Subordination and superordination results of p-valent analytic functions involving a linear operator

2017 ◽  
Vol 35 (2) ◽  
pp. 223 ◽  
Author(s):  
Tamer M. Seoudy
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc

In this paper we derive some subordination and superordination results for certain p-valent analytic functions in the open unit disc, which are acted upon by a class of a linear operator. Some of our results improve and generalize previously known results.

scholarly journals New sufficient conditions for starlikeness of analytic functions involving a fractional differintegral operator

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
J. K. Prajapat ◽  
R. K. Raina
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Fractional Differintegral ◽  
Class Of Functions ◽  
Fractional Differintegral Operator

AbstractIn this paper we apply a fractional differintegral operator to a class of analytic functions and derive certain new sufficient conditions for the starlikeness of this class of functions. The usefulness of the main results are depicted by deducing several interesting corollaries and relevances with some of the earlier results are also pointed out.

Majorization-Subordination Theorems for Locally Univalent Functions, II

1973 ◽  
Vol 25 (2) ◽  
pp. 420-425 ◽  
Author(s):  
Douglas Michael Campbell
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Family ◽  
Linear Invariant ◽  
Linear Invariant Family

Let denote the set of all normalized analytic univalent functions in the open unit disc D. Let f(z), F(z) and φ(z) be analytic in |z| < r. We say that f(z) is majorized by F(z) in we say that f(z) is subordinate to F(z) in where .Let be the set of all locally univalent (f’(z) ≠ 0) analytic functions in D with order ≦α which are of the form f(z) = z +… . The family is known as the universal linear invariant family of order α [6]. A concise summary of and introduction to properties of linear invariant families which relate to the following material is contained in [1]. The present paper contains the proofs of some of the results announced in [1]

scholarly journals Certain Conditions for Starlikeness of Analytic Functions of Koebe Type

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Saibah Siregar ◽  
Maslina Darus
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Subordination Result ◽  
Jack’S Lemma ◽  
Jack's Lemma

For , , we consider the of normalized analytic convex functions defined in the open unit disc . In this paper, we investigate the class , that is, , with is Koebe type, that is, . The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class of -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.

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