Coefficient estimate, distortion theorem, radii of starlikeness and convexity, closure theorems and hadamard product of functions belonging to this class are obtained. On harmonic combination of univalent functions obradovic, m. Oct 19, 2018 analogous to the biunivalent analytic functions, a function \g\in\sigma\ is said to be meromorphic and biunivalent if both g and \g1\ are meromorphic and univalent in. Elementary considerations for classes of meromorphic univalent. Z acn\2 meromorphic univalent functions defined by using convolution. Intuitively, a meromorphic function is a ratio of two wellbehaved holomorphic functions. Pdf coefficient estimates for meromorphic biunivalent functions. Let s denote the class of meromorphic univalent functions g of the form. Such a function will still be wellbehaved, except possibly at the points where the denominator of the fraction is zero. Dec 19, 2019 a meromorphic function is the ratio of two analytic functions, which are analytic with the exception of poles isolated singularities.
Let us define the hadamard product of two meromorphic univalent functions f z and g z by 1. Pdf coefficient estimates for a class of meromorphic bi. This paper establishes new criteria for meromorphic starlike univalent functions of the form. The authors also consider some closely related known or new corollaries and consequences of the main results presented in this paper. Coefficient estimates for a class of meromorphic bi univalent functions. The coefficient problem was investigated for various interesting subclasses of the meromorphic univalent functions see, e. If z is meromorphic at a point so then it is an elementary fact that the multivalent character of z in the neighborhood of z0 is like that of a power. Followed by brannan andtaha 3 see also 2, 20, srivastava et al. Multivalued function and its branches 76 unitiii 1. We obtain some interesting geometric properties according to coefficient inequality, growth and distortion theorems, radii of starlikeness and convexity for the functions in our subclass. Let us define the hadamard product of two meromorphic univalent functions f z. In the present investigation, certain subclasses of meromorphic biunivalent functions are introduced and estimates for the coefficients and of functions in the newly introduced subclasses are obtained. The hadamard product of more than two meromorphic functions can be defined similarly.
Coefficient estimates for a subclass of meromorphic bi. The term meromorphic univalent functions of complex order has been mentioned in some papers but they dont explain what it is. 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. A branch of complex analysis with classical roots, it is an active. By specializing cn and dn, representation theorms, bounds, convolution, geometric convolution, integral convolution and convex combinations for such functions have been determined.
Applications of the differential operator to a class of meromorphic. Some interesting properties of a subclass of meromorphic univalent functions defined by hadamard product author. Majorization problem for certain classes of meromorphic multivalent functions defined by differential operator. Historically 1, the classical polylogarithm function. Coefficient estimates for new subclasses of meromorphic bi. The function tr,f is called the characteristic function of fz.
Meromorphic univalent functions, integral operator, closure theorem, convex combination, distortion bound, partial sums and neighborhood property. Multiplier family of univalent harmonic meromorphic functions. Pdf meromorphic univalent functions with positive coeffcients. In this article, we consider functions meromorphic in the unit disk. In the case of meromorphic functions and surfaces spread over the sphere, conditions b and c are still equivalent. A representation theorem for functions in the class, as well. On classes of meromorphic locally univalent functions defined. Relevant connections of the results obtained here with various known results for meromorphic univalent functions are indicated. On a subclass of meromorphic univalent functions involving. This site is like a library, use search box in the widget to get ebook that you want. Department of mathematics, faculty of science, jazan university, jazan, saudi arabia. On certain subclass of meromorphic univalent functions 55 5 radii of starlikeness and convexity the radii of starlikeness and convexity for the class s.
In this article, we consider a class denoted by which consists of functions f that are holomorphic in the unit disc punctured at a point where f has. The hadamard product of meromorphic univalent functions. Pdf the hadamard product of meromorphic univalent functions. By this we mean that for some integer n, the function. 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. The decomposition of meromorphic functions into rational functions of univalent functions by lynn h. Waggas galib atshan, thamer khalil mohammed subject.
A new subclass of meromorphic biunivalent functions. The aim of this article is to study a multiplier family of univalent harmonic meromorphic functions using the sequences cn and dn of positive real numbers. Meromorphic univalent functions with positive coefficients. On a new subclass of meromorphic univalent functions. The class of all meromorphic and biunivalent functions is denoted by. Hadamard product of certain harmonic univalent meromorphic. Unicity of meromorphic functions of class a chen, tenging and chen, kengyan, taiwanese journal of mathematics, 2008. The hadamard product of meromorphic univalent functions defined by using convolution. On subclass of meromorphic univalent function defined by.
Meromorphic univalent functions with positive coeffcients article pdf available in bulletin of the australian mathematical society 3202. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. A regular or meromorphic function in a domain of the extended complex plane such that whenever, that is, is a onetoone mapping from into. Majorization problem for certain classes of meromorphic. The main object of the present paper is to, introduce the. 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. Coefficient estimates for a class of meromorphic bi univalent functions article pdf available in comptes rendus mathematique may 20 with 167 reads how we measure reads. Multivalent function, and in particular valent functions, are a generalization of univalent functions. We begin by giving some wellknown notations and preliminary results on the class of meromorphic functions and also the basic knowledge of subordination. Pdf on the coefficients of meromorphic univalent functions. Pdf certain classes of meromorphic univalent functions with. Harmonic functions, meromorphic functions, univalent functions, sensepreserving. Coefficient estimates for a class of meromorphic biunivalent functions. What is the meaning of a meromorphic univalent function.
On sandwich theorems for univalent meromorphic functions involving integral operator waggas galib atshan and khudair o. Some interesting properties of a subclass of meromorphic. Estimating coefficients for certain subclasses of meromorphic. If this is the first time you use this feature, you will be asked to authorise cambridge core to connect with your account. The class of these bi univalent functions is denoted by. Click download or read online button to get univalent functions book now. Meromorphic univalent functions with positive coefficients bulletin. On a new subclass of meromorphic univalent functions defined. Aa defined in the annulus 0 find, read and cite all the research you need on researchgate. New criteria for meromorphic starlike univalent functions. On the taylor coefficients of a subclass of meromorphic univalent. On meromorphic and univalent functions abe, hitoshi, proceedings of the japan academy, series a, mathematical sciences, 1987. On classes of meromorphic locally univalent functions.
The theory of univalent functions is a fascinating interplay of geometry and analysis, directed primarily toward extremal problems. On certain subclasses of meromorphic univalent funtions. In this paper, we define a new subclass of meromorphic closetoconvex univalent functions defined in the punctured open unit disc by using a differential. Sufficient conditions for subordination of meromorphic. In the second paragraph are presented some special classes of univalent functions. Pdf on a subclass of meromorphic univalent functions. Joudah, subclass of meromorphic univalent functions defined by hadamard product with multiplier transformation, int. An holomorphic function or meromorphic and injective on the domain dfrom c is univalent on d. Some inclusion results, convolution properties and several other properties of this class are studied. New criteria for meromorphic starlike univalent functions volume 43 issue 1 b. In this article, we follow the similar approach by introducing a differential operator of meromorphic functions in the punctured disk.
Applications of the differential operator to a class of. And in 1971, duren 2 gave an elementary proof of the inequality b n. Meromorphic univalent functions with positive coefficients volume 32 issue 2 m. We denote by h ud the set of univalent functions on the domain d. In the present investigation, certain subclasses of meromorphic biunivalent functions are introduced and estimates for the coefficients b 0 and b 1 of functions in the newly introduced subclasses are obtained. On the coefficients of meromorphic univalent functions. We present some typical problems of geometrical function theory and give elementary solutions in the case of the above functions. Univalent functions download ebook pdf, epub, tuebl, mobi. 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. In this paper, we define a new subclass of meromorphic closetoconvex univalent functions defined in the punctured open unit disc by using a differential operator. May 27, 2019 in this article, we consider functions meromorphic in the unit disk. Meromorphic univalent function, hadmard product, convex function, starlike function. On sandwich theorems for univalent meromorphic functions.
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