Piggyback-Dualitäten

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.

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A unified class of harmonic functions with varying argument of coefficients

Filomat ◽

10.2298/fil1804349s ◽

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.

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

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v38i6.40530 ◽

2019 ◽

Vol 38 (6) ◽

pp. 33-42 ◽

Cited By ~ 2

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

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A Class of Analytic Functions with Missing Coefficients

Abstract and Applied Analysis ◽

10.1155/2011/456729 ◽

2011 ◽

Vol 2011 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

Ding-Gong Yang ◽

Jin-Lin Liu

Keyword(s):

Unit Disk ◽

Analytic Functions ◽

Open Unit ◽

Open Unit Disk ◽

Coefficient Estimates ◽

Sharp Bounds ◽

Radius Of Convexity ◽

Convolution Properties ◽

Class Of Functions

Let and denote the class of functions of the form which are analytic in the open unit disk and satisfy the following subordination condition , for, for. We obtain sharp bounds on , and coefficient estimates for functions belonging to the class . Conditions for univalency and starlikeness, convolution properties, and the radius of convexity are also considered.

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

Georgian Mathematical Journal ◽

10.1515/gmj-2018-0016 ◽

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].

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Applications on a subclass of β-uniformly starlike functions connected with q-Borel distribution

Asian-European Journal of Mathematics ◽

10.1142/s1793557122501583 ◽

2021 ◽

Author(s):

Sheza M. El-Deeb ◽

G. Murugusundaramoorthy

Keyword(s):

Starlike Functions ◽

Coefficient Estimates ◽

Linear Combinations ◽

Distortion Theorems ◽

Uniformly Starlike Functions ◽

Uniformly Starlike

The aim of this paper is to define the operator of [Formula: see text]-derivative based upon the Borel distribution and by using this operator, we familiarize a new subclass of [Formula: see text]-uniformly starlike functions [Formula: see text]-[Formula: see text] Further, we obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions [Formula: see text]-[Formula: see text] We also determine the second Hankel inequality for functions belonging to this subclass.

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Harmonic Starlike Functions with Respect to Symmetric Points

Axioms ◽

10.3390/axioms9010003 ◽

2019 ◽

Vol 9 (1) ◽

pp. 3 ◽

Cited By ~ 2

Author(s):

Nak Eun Cho ◽

Jacek Dziok

Keyword(s):

Integral Representation ◽

Starlike Functions ◽

Coefficient Estimates ◽

Distortion Theorems ◽

Harmonic Starlike ◽

Symmetric Points

In the paper we define classes of harmonic starlike functions with respect to symmetric points and obtain some analytic conditions for these classes of functions. Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are also obtained.

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Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions

Nagoya Mathematical Journal ◽

10.1017/s0027763000000854 ◽

1987 ◽

Vol 106 ◽

pp. 1-28 ◽

Cited By ~ 48

Author(s):

H. M. Srivastava ◽

Shigeyoshi Owa

Keyword(s):

Fractional Calculus ◽

Analytic Functions ◽

Hypergeometric Functions ◽

Linear Operators ◽

Coefficient Estimates ◽

Hadamard Products ◽

Generalized Hypergeometric Functions ◽

Hypergeometric Type ◽

Distortion Theorems ◽

Characterization Theorems

By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disk are introduced and studied systematically. The various results presented here include, for example, a number of coefficient estimates and distortion theorems for functions belonging to these subclasses, some interesting relationships between these subclasses, and a wide variety of characterization theorems involving a certain functional, some general functions of hypergeometric type, and operators of fractional calculus. Some of the coefficient estimates obtained here are fruitfully applied in the investigation of certain subclasses of analytic functions with fixed finitely many coefficients.

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Estimates for coefficients of certain analytic functions

Filomat ◽

10.2298/fil1711539r ◽

2017 ◽

Vol 31 (11) ◽

pp. 3539-3552 ◽

Cited By ~ 1

Author(s):

V. Ravichandran ◽

Shelly Verma

Keyword(s):

Convex Function ◽

Convex Functions ◽

Analytic Functions ◽

Starlike Functions ◽

Coefficient Estimates ◽

Coefficient Problem ◽

Inverse Coefficient Problem ◽

Coefficient Bounds ◽

Inverse Functions ◽

Inverse Coefficient

For -1 ? B ? 1 and A > B, let S*[A,B] denote the class of generalized Janowski starlike functions consisting of all normalized analytic functions f defined by the subordination z f'(z)/f(z)< (1+Az)/(1+Bz) (?z?<1). For -1 ? B ? 1 < A, we investigate the inverse coefficient problem for functions in the class S*[A,B] and its meromorphic counter part. Also, for -1 ? B ? 1 < A, the sharp bounds for first five coefficients for inverse functions of generalized Janowski convex functions are determined. A simple and precise proof for inverse coefficient estimations for generalized Janowski convex functions is provided for the case A = 2?-1(?>1) and B = 1. As an application, for F:= f-1, A = 2?-1 (?>1) and B = 1, the sharp coefficient bounds of F/F' are obtained when f is a generalized Janowski starlike or generalized Janowski convex function. Further, we provide the sharp coefficient estimates for inverse functions of normalized analytic functions f satisfying f'(z)< (1+z)/(1+Bz) (?z? < 1, -1 ? B < 1).

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Bounded Doubly Close-to-Convex Functions

Abstract and Applied Analysis ◽

10.1155/2014/804095 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Dorina Răducanu

Keyword(s):

Convex Functions ◽

Starlike Functions ◽

Coefficient Bounds ◽

New Class ◽

Radius Of Convexity ◽

Distortion Theorems

We consider a new classCC(α,β)of bounded doubly close-to-convex functions. Coefficient bounds, distortion theorems, and radius of convexity for the classCC(α,β)are investigated. A corresponding class of doubly close-to-starlike functionsS*S(α,β)is also considered.

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