Neighborhoods of univalent functions
Stephan Ruscheweyh
- Vol. 81, Iss: 4, pp 521-527
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The article was published on 1981-04-01 and is currently open access. It has received 289 citations till now. The article focuses on the topics: Univalent function & Hadamard product.read more
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A Linear Operator and Associated Families of Meromorphically Multivalent Functions
Jin-Lin Liu,Hari M. Srivastava +1 more
TL;DR: In this paper, a linear operator is defined by means of the Hadamard product (or convolution) and two families of meromorphically multivalent functions are introduced and investigated.
Journal ArticleDOI
Classes of meromorphically multivalent functions associated with the generalized hypergeometric function
Jin-Lin Liu,Hari M. Srivastava +1 more
TL;DR: In this paper, a linear operator is defined by means of a Hadamard product involving the generalized hypergeometric function, and the properties and characteristics of two novel classes of meromorphically multivalent functions are investigated.
Journal ArticleDOI
Neighborhoods of a class of analytic functions with negative coefficients
TL;DR: By making use of the familiar concept of neighborhoods of analytic functions, the authors prove several inclusion relations associated with the (n, δ)-neighborhoods of various subclasses of starlike and convex functions of complex order.
Journal ArticleDOI
Neighborhoods of a certain family of multivalent functions with negative coefficients
TL;DR: In this paper, the authors prove coefficient bounds and distortion inequalities for the (n, δ)-neighborhoods of a family of multivalent functions with negative coefficients, which is defined by means of a certain nonhomogeneous Cauchy-Euler differential equation.
Journal Article
A generalized operator involving the $q$-hypergeometric function
Aabed Mohammed,Maslina Darus +1 more
TL;DR: In this paper, a new general operator for q-hypergeometric functions is introduced and a subclass of analytic functions is defined, which generalizes well known classes of starlike and convex functions.
References
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Hadamard products of Schlicht functions and the Pólya-Schoenberg conjecture
St. Ruscheweyh,T. Sheil-Small +1 more
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Univalent functions and nonanalytic curves
TL;DR: In this paper, the right sides of the power series can not be increased without destroying the starlikeness and convexity of the image regions, which was first discovered by Alexander [I], but according to Remak's proof contains an error.