Starlike functions of complex order 1 introduction citeseerx. Citeseerx document details isaac councill, lee giles, pradeep teregowda. We are committed to sharing findings related to covid19 as quickly and safely as possible. This book provides valuable insights into complex analysis, dynamical systems, geometric function theory and operator theory. Re be the class of starlike functions of order 0, and analogous to the class, for g we define the class of meromorphic functions g then, obtaining some subordination results on functions in this class. Majorization by starlike functions of complex order request pdf. The interesting geometric properties of these function classes were extensively studied by kanas et al. Basic and fractional qcalculus and associated feketeszego. This book is directed at introducing and bringing up to date current research in the area of univalent functions, with an emphasis on the important subclasses, thus providing an. In the present paper, we introduced two new subclasses of bi starlike and biconvex function of complex order involving double zeta functions in the open unit disc and obtained coefficient estimates for functions in these classes. We will be providing unlimited waivers of publication charges for accepted articles related to covid19. Jul 17, 2006 2010 certain subclasses of starlike functions of complex order involving generalized hypergeometric functions. A generalization of starlike functions of order alpha authors.
Pdf starlike functions of complex order with bounded radius. Starlike functions of complex order 559 2 results the results begin with a necessary and su. The purpose of this paper is to construct a manyparameter class of functions fc which includes the result 1. We note that the class of janowskis starlike functions of complex order contain many interesting subclasses of univalent functions. Starlike definition of starlike by the free dictionary.
A function which is regular and univalent in the disc, and maps onto a starlike domain with respect to. Formula 2 can be regarded as a generalization of the christoffelschwarz formula for mappings of the disc onto convex polygons let be the class of all convex functions in normalized by the conditions. Properties of harmonic meromorphic functions which are. In view of the wellknown riemann mapping theorem in classical complex analysis. Some properties for starlike functions with respect to k. We study various properties of this class including coe cient conditions, distortion bounds, extreme points, convex combination and nd their connection with the already known classes. We also obtain the sharp radius of starlikeness of the classfb, m. Also, majorization problems for starlike functions of complex order have recently been investigated by altintas et al. Nasr a m and aouf k mstarlike functions of complex order submitted 8 singh r 1968j. Starlike and prestarlike hypergeometric functions siam.
This paper defines and investigates a class of meromorphic univalent harmonic functions that are starlike of complex order with respect to conjugate points. Ams proceedings of the american mathematical society. The purpose of this paper is to give exact value of the radius of starlikeness and distortion theorem, koebe domain for the class of janowskis starlike functions of complex order. On some results for starlike functions of complex order. Uniformly harmonic starlike functions of complex order. We give necessary and sufficient conditions for the functions to be in ts.
The aim of this paper is to establish the coefficient estimates for the subclasses of starlike and convex functions with respect to symmetric points involving difference operator. C \ 0 of functions which are harmonic in the unit disc. The present paper aims to establish the first order differential subordination relations between functions with a positive real part and starlike functions related to the bell numbers. A generalization of starlike functions of order alpha open. Some properties for \\alpha\starlike functions with. 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. By means of a differential operator, we introduce and investigate some new subclasses of valently analytic functions with negative coefficients, which are starlike or convex of complex order. In this paper, the authors introduce a new subclass of meromorphic q starlike functions which are associated with the janowski functions. Some general classes of qstarlike functions associated. Numerous examples have been given throughout the book, and there is also a set of miscellaneous examples, arranged to correspond with. Koebe domain of starlike functions of complex order with. Certain subclass of analytic functions with complex order. Oct 20, 2015 in addition, the complex orders just sit in the complex order book and there is no connection to the listed quotes in the regular order book. Differential sandwichtype results for starlike functions.
Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are also obtained. Apart from establishing coefficient bounds for these classes, we establish inclusion relationships involving n. Linearization models for complex dynamical systems topics. Multivalued starlike functions of complex order 21 therefore, we conclude that, for any real. Coefficient bounds for certain subclasses of starlike functions of. Sharp upper bounds of for the function belonging to certain subclass of starlike functions with respect to symmetric points of complex order are obtained. An introduction to the theory of complex variables. The authors investigate several majorization problems involving starlike and convex functions 01 complex order as well as functions belonging to a certain class. The author obtain coefficient conditions, growth result, extreme points, convolution and convex combinations. Axioms free fulltext harmonic starlike functions with. H denote the class of functions f which are harmonic, meromorphic, orientation preserving and univalent in a. Two new subclasses of analytic functions of complex order are introduced.
Certain subclasses of starlike functions of complex order involving generalized hypergeometric functions. A function, in,, regular in, is starlike in this disc if and only if it satisfies the condition the family of starlike functions in, normalized so that, forms the class. On certain multivalent starlike or convex functions with. In addition, several sharp radii estimates for functions in the class of starlike functions associated with the bell numbers are determined. Majorization by starlike functions of complex order. Univalent functions download ebook pdf, epub, tuebl, mobi. This book deals with the theory of convex and starlike biholomorphic mappings in several complex variables.
Criteria for starlike and convex functions of order. Coefficient estimates of new classes of qstarlike and qconvex functions of complex order author. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. Feketeszego inequalities for certain subclasses of starlike and convex functions of complex order associated with quasisubordination. Several new or known consequences of the results are also pointed out. Bounded starlike functions of complex order springerlink.
Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out. Analytic functions, starlike functions of complex order, convex functions of complex order, starlike, ksymmetric points, subordination. Certain subclasses of starlike functions of complex order. Assume that f lies in the class of starlike functions of order. The main object of the paper is to determine coefficient bounds for the class, and obtain the exact results.
American mathematical society 201 charles street providence, rhode island 0290422 4014554000 or 8003214267 ams, american mathematical society, the tricolored ams logo, and advancing research, creating connections, are trademarks and services marks of the american mathematical society and registered in the u. Hence hz is the centroid of a positive mass distribution of total mass one on the curvezz and so lies in the convex hull of this curve. Certain subclasses of analytic functions with complex order. Intended for a broad spectrum of readers, ranging from undergraduate and graduate mathematics students to active researchers, it offers extensive coverage of recent advances in geometric function theory, including the theory of starlike and spirallike functions with. Are treated some classes of univalent functions, the di erential subordinations and superordinations methods, loewner chains method and integral operators by s al. A is said to be a starlike function of order b b 0, complex, if and only if zz 0. This is the first book which systematically studies this topic. This book is designed for students who, having acquired a good working knowledge of the calculus, desire to become acquainted with the theory of functions of a complex variable, and with the principal applications of that theory. Convex and starlike mappings in several complex variables. As an analogue to the complex n th starlikeness of a complex order we may introduce the notion of n th convexity of a complex order as follows. Yasar polatoglu, metin bolcal, arzu sen submitted on 1 aug 2000. Coefficient estimates of new classes of qstarlike and q.
The main purpose of this paper is to introduce a class ts. Feketeszego inequalities for certain subclasses of. Introduction let a denote the class of functions of the form f. Pdf a proof of halls conjecture on length of ray images. Symmetry free fulltext starlike functions related to the. The study of univalent functions dates back to the early years of the 20th century, and is one of the most popular research areas in complex analysis.
Jul 18, 2006 2018 starlike functions of complex order with bounded radius rotation by using quantum calculus. Sahoo submitted on 15 apr 2014 v1, last revised 11 sep 2015 this version, v2. Feketeszego inequalities for starlike functions with respect to. Koebe domain of starlike functions of complex order with montel normalization. In this paper, we introduce a family of harmonic parabolic starlike functions of complex order in the unit disc and coe. A generalization of starlike functions of order alpha sarita agrawal. That was a problem, because there could be a spread that looks like it could execute but it doesnt, says henry schwartz, ceo of tradealert. Pdf a generalization of starlike functions of order alpha. This book is directed at introducing and bringing up to date current research in the area of univalent functions, with an emphasis on the important subclasses, thus providing an accessible resource suitable for both beginning and experienced.
Bistarlike function of complex order associated with. On strongly starlike and convex functions of order and type. Srivastava, some majorization problems associated with pvalently starlike and convex functions of complex order, east asian math. A certain subclass of meromorphically q starlike functions. In this paper, we introduce and study some subclasses of pvalently analytic functions. In this paper we define a new subclass of starlike functions of complex order based on qhypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class ts ksi alpha, beta, gamma. Also sharp coefficient bounds are established for functions infb, m. Certain subclasses of starlike and convex functions of complex order v ravichandran, y polatoglu, m bolcal, a sen hacettepe journal of mathematics and statistics 34, 915, 2005. Some other important qgeneralizations and qextensions of complex operators are the.
Magesh, starlike and convex functions of complex order involving the dzioksrivastava operator, integral transforms and special functions, vol. On classes of functions related to starlike functions with respect to symmetric conjugate points defined by a fractional differential operator, complex anal. Coefficient estimates for functions in these classes and radii of closeto convexity, starlikeness and convexity are obtained. Coefficient bounds for some families of starlike and convex functions. Univalent functions and orthonormal systems download ebook. Also certain applications based on these results for subclasses of univalent functions defined by convolution are given. This book is directed at introducing and bringing up to date current research in the area of univalent functions, with an emphasis on the important subclasses, thus providing an accessible. Univalent functions of one complex variable in this chapter are presented notions and elementary results from the geometric theory of univalent functions of one complex variable. Convex function of a complex variable encyclopedia of. International journal of mathematics and mathematical sciences 2010, 112.
A generalization of starlike functions of order alpha. This paper defines and investigates a family of complexvalued harmonic functions that are orientation preserving and univalent in d and are related to the functions starlike of complex order. Certain bound for starlike and convex functions with. There is a close interrelation between analytic functions and harmonic functions. Some results on the janowskis starlike functions of. The class, fpm of bounded starlike functions of complex order was introduced by nasr and aouf 4. A function f member of a is said to be starlike in the open unit disk e if it is univalent in e and fe is a starlike domain. Bistarlike function of complex order associated with double.
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