81 research outputs found
A generalization of starlike functions of order alpha
For every and we define a class of analytic
functions, the so-called -starlike functions of order , on the open
unit disk. We study this class of functions and explore some inclusion
properties with the well-known class of starlike functions of order .
The paper is also devoted to the discussion on the Herglotz representation
formula for analytic functions when is -starlike of
order . As an application we also discuss the Bieberbach conjecture
problem for the -starlike functions of order . Further application
includes the study of the order of -starlikeness of the well-known basic
hypergeometric functions introduced by Heine.Comment: 13 pages, 4 figures, submitted to a journa
Coefficient estimates for some classes of functions associated with -function theory
In this paper, for every , we obtain the Herglotz representation
theorem and discuss the Bieberbach type problem for the class of -convex
functions of order . In addition, we discuss the
Fekete-szeg\"o problem and the Hankel determinant problem for the class of
-starlike functions, leading to couple of conjectures for the class of
-starlike functions of order .Comment: 12 page
On the Bohr inequality
The Bohr inequality, first introduced by Harald Bohr in 1914, deals with
finding the largest radius , , such that holds whenever in the unit disk
of the complex plane. The exact value of this largest radius,
known as the \emph{Bohr radius}, has been established to be This paper
surveys recent advances and generalizations on the Bohr inequality. It
discusses the Bohr radius for certain power series in as well as
for analytic functions from into particular domains. These domains
include the punctured unit disk, the exterior of the closed unit disk, and
concave wedge-domains. The analogous Bohr radius is also studied for harmonic
and starlike logharmonic mappings in The Bohr phenomenon which is
described in terms of the Euclidean distance is further investigated using the
spherical chordal metric and the hyperbolic metric. The exposition concludes
with a discussion on the -dimensional Bohr radius
A subclass of meromorphic Janowski-type multivalent q-starlike functions involving a q-differential operator
Keeping in view the latest trends toward quantum calculus, due to its various applications in physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions in Janowski domain with the help of the q-differential operator. Furthermore, we investigate some useful geometric and algebraic properties of these functions. We discuss sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikeness, radius of convexity, inclusion property, and convex combinations via some examples and, for some particular cases of the parameters defined, show the credibility of these results. © 2022, The Author(s)
Subclasses of univalent functions related with functions of bounded radius rotation
This investigation is in twofold. Firstly, a comprehensive generalization of starlike functions is initiated. This notion gives more insight to the study of functions with bounded radius rotation. In this direction, we examine the geometric characterization of this class, which includes the inclusion, radius results and integral preserving properties. On the other hand, the class of functions that extend the idea of close-toconvex functions is introduced. Also, a necessary condition, radius results, coefficient results and closure property under convex convolution for this novel class are investigated. Overall, some alluring consequences of our results are also presented.Publisher's Versio
Mapping properties of basic hypergeometric functions
It is known that the ratio of Gaussian hypergeometric functions can be represented by means of g-fractions. In this work, the ratio of q-hypergeometric functions are represented by means of g-fractions that lead to certain results on q-starlikeness of the q-hypergeometric
functions defined on the open unit disk. Corresponding results for the q-convex case are also obtained
Certain Properties of a Class of Close-to-Convex Functions Related to Conic Domains
We aim to define a new class of close-to-convex functions which is related to conic domains. Many interesting properties such as sufficiency criteria, inclusion results, and integral preserving properties are investigated here. Some interesting consequences of our results are also observed
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