scholarly journals Some Properties of Certain Multivalent Analytic Functions Involving the Cătas Operator

2011 ◽  
Vol 2011 ◽  
pp. 1-25
Author(s):  
E. A. Elrifai ◽  
H. E. Darwish ◽  
A. R. Ahmed
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Principle Of Subordination ◽  
Distortion Theorems ◽  
Convolution Properties

We introduce a certain subclass of multivalent analytic functions by making use of the principle of subordination between these functions and Cătas operator. Such results as subordination and superordination properties, convolution properties, inclusion relationships, distortion theorems, inequality properties, and sufficient conditions for multivalent starlikeness are provide. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained.

ON CERTAIN SUBCLASS OF p-VALENT NON-BAZILEVIC FUNCTIONS DEFINED BY THE DZIOK–SRIVASTAVA OPERATOR

2013 ◽  
Vol 06 (03) ◽  
pp. 1350032
Author(s):  
T. M. Seoudy ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Principle Of Subordination ◽  
Distortion Theorems ◽  
Convolution Properties ◽  
Bazilevic Functions

By making use of the principle of subordination and Dziok–Srivastava operator, we introduce a certain subclass of p-valent non-Bazilevic analytic functions. Such results as subordination and superordination properties, convolution properties, distortion theorems and inequality properties, are proved.

Results of differential subordination for a unified subclass of analytic functions defined using generalized Ruscheweyh derivative operator

2019 ◽  
Vol 12 (03) ◽  
pp. 1950035
Author(s):  
Ritu Agarwal ◽  
G. S. Paliwal ◽  
Parany Goswami
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Sandwich Theorem ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Principle Of Subordination ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we introduce a unified subclass of analytic functions by making use of the principle of subordination, involving generalized Ruscheweyh Derivative operator [Formula: see text]. The properties such as inclusion relationships, distortion theorems, coefficient inequalities and differential sandwich theorem for the above class have been discussed.

scholarly journals Upper and lower bounds of integral operator defined by the fractional hypergeometric function

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Muhammad Zaini Ahmad ◽  
Hiba F. Al-Janaby
Keyword(s):  
Integral Operator ◽  
Hypergeometric Function ◽  
Lower Bounds ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Holomorphic Functions ◽  
Upper And Lower Bounds ◽  
Distortion Theorems

AbstractIn this article, we impose some studies with applications for generalized integral operators for normalized holomorphic functions. By using the further extension of the extended Gauss hypergeometric functions, new subclasses of analytic functions containing extended Noor integral operator are introduced. Some characteristics of these functions are imposed, involving coefficient bounds and distortion theorems. Further, sufficient conditions for subordination and superordination are illustrated.

scholarly journals A unified class of harmonic functions with varying argument of coefficients

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1349-1357
Author(s):  
Grigore Sǎlǎgean ◽  
Páll-Szabó Orsolya
Keyword(s):  
Harmonic Functions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Closure Properties ◽  
Principle Of Subordination ◽  
Distortion Theorems ◽  
Convolution Properties

In this paper we investigate several classes of harmonic functions with varying argument of coefficients which are defined by means of the principle of subordination between harmonic functions. Properties such as the coefficient estimates, distortion theorems, convolution properties, radii of convexity, starlikeness and the closure properties of these classes under the generalized Bernardi-Libera-Livingston integral operators are investigated.

scholarly journals Some properties of a class of analytic functions involving a new generalized differential operator

2019 ◽  
Vol 38 (6) ◽  
pp. 33-42 ◽  
Author(s):  
A. A. Amourah ◽  
Feras Yousef
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Generalized Differential ◽  
Growth And Distortion Theorems

In the present paper, we introduce a new generalized differentialoperator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ defined on the openunit disc $U=\left\{ z\in%%TCIMACRO{\U{2102} }%%BeginExpansion\mathbb{C}:\left\vert z\right\vert <1\right\} $. A novel subclass $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ by means of the operator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ is also introduced. Coefficient estimates, growth and distortion theorems, closuretheorems, and class preserving integral operators for functions in the class $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ are discussed. Furthermore, sufficient conditions for close-to-convexity, starlikeness, and convexity for functions in the class $\Om are obtained

scholarly journals Piggyback-Dualitäten

1985 ◽  
Vol 32 (1) ◽  
pp. 1-32 ◽  
Author(s):  
B.A. Davey ◽  
H. Werner
Keyword(s):  
Series Expansion ◽  
Analytic Functions ◽  
Laurent Series ◽  
Integral Operators ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Radius Of Convexity ◽  
Distortion Theorems ◽  
Convolution Properties

For the class of meromorphically starlike functions of prescribed order, the concept of type has been introduced. A characterization of meromorphically starlike functions of order α and type β has been obtained when the coefficients in its Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, radius of convexity estimates, integral operators, convolution properties et cetera for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients.

Properties of Certain Multivalent Analytic Functions Associated with the Lemniscate of Bernoulli

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 160
Author(s):  
Likai Liu ◽  
Jin-Lin Liu
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Lemniscate Of Bernoulli

Using differential subordination, we consider conditions of β so that some multivalent analytic functions are subordinate to (1+z)γ (0<γ≤1). Notably, these results are applied to derive sufficient conditions for f∈A to satisfy the condition zf′(z)f(z)2−1<1. Several previous results are extended.

Convolution properties for certain subclass of analytic functions

2013 ◽  
Author(s):  
Norlyda Mohamed ◽  
Daud Mohamad ◽  
Shaharuddin Cik Soh
Keyword(s):  
Analytic Functions ◽  
Convolution Properties

scholarly journals QKtype spaces of analytic functions

2006 ◽  
Vol 4 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Hasi Wulan ◽  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient Conditions ◽  
Type Space ◽  
Necessary And Sufficient ◽  
Spaces Of Analytic Functions

For a nondecreasing functionK:[0,8)?[0,8)and0<p<8,-2<q<8, we introduceQK(p,q), aQKtype space of functions analytic in the unit disk and study the characterizations ofQK(p,q). Necessary and sufficient conditions onKsuch thatQK(p,q)become some known spaces are given.

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