288 research outputs found
Ruscheweyh – Type Harmonic Functions Associated with Probabilities of the Generalized Distribution and Sigmoid Function Defined by q- differential Operators
A class of Ruscheweyh – type harmonic functions associated with both sigmoid function and probabilities of the generalized distribution series is defined using differential operators. We then establish properties of the class such as coefficient estimate, distortion theorem, extreme point, and convex combination condition. Several applications of our results are obtained as corollaries by varying various parameters involved
Geometrical Theory of Analytic Functions
The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria
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
Majorization for a Class of Analytic Functions Defined by q
We introduce a new class of multivalent analytic functions defined by using q-differentiation and fractional q-calculus operators. Further, we investigate majorization properties for functions belonging to this class. Also, we point out some new and known consequences of our main result
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