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 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.

scholarly journals Meromorphic univalent functions with positive coefficients

1985 ◽  
Vol 32 (2) ◽  
pp. 161-176 ◽  
Author(s):  
M.L. Mogra ◽  
T.R. Reddy ◽  
O.P. Juneja
Keyword(s):  
Univalent Functions ◽  
Integral Operators ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Radius Of Convexity ◽  
Distortion Theorems ◽  
Convolution Properties ◽  
Positive Coefficients ◽  
Meromorphic Univalent Functions

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.

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.

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 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.

scholarly journals ON CERTAIN SUBCLASS OF UNIVALENT FUNCTIONS IN THE UNIT DISC I

1995 ◽  
Vol 26 (4) ◽  
pp. 299-312
Author(s):  
M. K. AOUF ◽  
A. SHAMANDY ◽  
M. F. YASSEN
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Closure Theorems ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Analytic And Univalent Functions

The object of the present paper is to derive several interesting proper- ties of the class $P_n(\alpha, \beta, \gamma)$ consisting of analytic and univalent functions with neg- ative coefficients. Coefficient estimates, distortion theorems and closure theorems of functions in the class $P_n(\alpha, \beta, \gamma)$ are determined. Also radii of close-to-convexity, starlikeness and convexity and integral operators are determined.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

New subclasses of analytic functions defined by convolution involving the hypergeometric function and the Owa–Srivastava operator

2019 ◽  
Vol 26 (3) ◽  
pp. 449-458
Author(s):  
Khalida Inayat Noor ◽  
Rashid Murtaza ◽  
Janusz Sokół
Keyword(s):  
Hypergeometric Function ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Integral Operators ◽  
Generalized Hypergeometric Functions ◽  
Convolution Properties ◽  
Appl Math ◽  
Inclusion Results

Abstract In the present paper we introduce a new convolution operator on the class of all normalized analytic functions in {|z|<1} , by using the hypergeometric function and the Owa–Srivastava operator {\Omega^{\alpha}} defined in [S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 1987, 5, 1057–1077]. This operator is a generalization of the operators defined in [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365] and [K. I. Noor, Integral operators defined by convolution with hypergeometric functions, Appl. Math. Comput. 182 2006, 2, 1872–1881]. Also we introduce some new subclasses of analytic functions using this operator and we discuss some interesting results, such as inclusion results and convolution properties. Our results generalize the results of [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365].

scholarly journals A Class of p-valent Functions in the Punctured Disc

2019 ◽  
pp. 473-481
Author(s):  
Olubunmi A. Fadipe-Joseph ◽  
K. O. Dada
Keyword(s):  
Differential Operator ◽  
Coefficient Estimates ◽  
Alpha Beta ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

Motivated by Aouf differential operator, a class $F_{\lambda, p}^{n}\left ( \alpha , \beta , \gamma \right )$ of p-valent functions in the punctured disc $U^{*}=\left \{ z:0<\left | z \right |<1 \right \}=U\setminus \left \{ 0 \right \} $ is defined. The coefficient estimates, growth and distortion theorems for the class are obtained.

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