QA443 : On Convolution over Harmonic and Univalent Functions
Thesis > Central Library of Shahrood University > Mathematical Sciences > PhD > 2018
Authors:
Abstarct: There are a few examples of uniformly starlike (convex) analytic functions and fully-starlike (fully-convex) harmonic functions, although we pose some examples in new class, uniformly starlike (convex) harmonic functions, any way the functions in new classes are rare and worthy as well. Furthermore we give necessary and sufficient conditions for a function to be in these classes. We mention recently works in this area.
The convolution or Hadamard product is a additional tool in univalent functions classes investigation. Previous results with convolution showed that this is a effective tool with powerful ability in univalent functions classes and with harmonic function, like generalizations of previous subclasses, convolution on harmonic classes like starlike, convex and close-to-convex families and so on. Recent works which have done by some authors in last decade, show ability and power of this method. We use convolution to obtain our results in new classes.
At last we discuss about bi-univalent functions as a subclass of S , more recently El-Ashwah introduced two subclasses of bi-univalent function class ∑ and obtained non-sharp estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3| of functions in each of these subclasses. We generalize her classes to new class of bi-univalent function with a convolution form and find the coefficients |a2| and |a3| of new class.
In brief,
• The work is devoted to the study of certain subclasses of analytic and harmonic univalent complex functions in the unit disk D .
• Certain classes of univalent starlike and convex functions are introduced.
• These analytic and harmonic classes provide a unified treatment to new subclasses.
• Main results are derived from Inclusion and convolution properties on new subclasses.
• New bi-univalent subclass is introduced and initial coefficients bound are derived using Caratheodory lemma and subordination.
Keywords:
#Univalent function #Uniformly starlike function #Uniformly convex function #Fully-starlike function #Fully-convex function #Bi-Univalent function #Convolution #Subordination Link
Keeping place: Central Library of Shahrood University
Visitor:
Keeping place: Central Library of Shahrood University
Visitor: