Abstract and Applied Analysis

Analytic and Harmonic Univalent Functions


Status
Published

Lead Editor

1University of Delhi, Delhi, India

2Kent State University, Burton, OH, USA

3Universiti Sains Malaysia, Penang, Malaysia


Analytic and Harmonic Univalent Functions

Description

The classical theory of analytic univalent functions is one of the oldest and beautiful subjects in geometric function theory. It was born around the turn of the twentieth century and has remained an active field of current research. A famous problem in this field was the Bieberbach conjecture posed in 1916 on the size of the moduli of the Taylor coefficients, which was affirmatively settled by de Branges in 1985. Toward its resolution, the conjecture inspired the development of ingenious mathematical tools with important influence, including Lowner’s parametric representation method, the area method, Grunsky inequalities, and methods of variations.

The study of planar harmonic univalent mappings, initially by differential geometers in the representation of minimal surfaces, has gained great interest as an active area of research in geometric function theory after the seminal 1984 paper by Clunie and Sheil-Small. It lays the foundation for the study of harmonic univalent mappings over the unit disk as a generalization of analytic univalent functions. Although analogues of the classical growth and distortion theorems, covering theorems, and coefficient estimates are known for suitably normalized harmonic univalent mappings, still many fundamental questions and conjectures remain unresolved in this area. There is a great expectation that the “harmonic Koebe function” will play the extremal role in many of these problems, much like the role played by the Koebe function in the classical theory of analytic univalent functions.

This special issue will publish original articles as well as review articles in the classical theory of analytic univalent functions, harmonic univalent functions, and their connections to produce deeper insights and better understanding.

Potential topics include, but are not limited to:

  • Univalent and multivalent analytic functions
  • Differential subordination and superordination
  • Entire and meromorphic functions
  • Geometric function theory in several complex variables
  • Harmonic univalent functions
  • Quasiconformal mappings

Articles

  • Special Issue
  • - Volume 2014
  • - Article ID 578214
  • - Editorial

Analytic and Harmonic Univalent Functions

V. Ravichandran | Om P. Ahuja | Rosihan M. Ali
  • Special Issue
  • - Volume 2014
  • - Article ID 601507
  • - Research Article

A Note on Entire Functions That Share Two Small Functions

Jun-Fan Chen
  • Special Issue
  • - Volume 2014
  • - Article ID 454152
  • - Research Article

Radius Constants for Functions with the Prescribed Coefficient Bounds

Om P. Ahuja | Sumit Nagpal | V. Ravichandran
  • Special Issue
  • - Volume 2014
  • - Article ID 792175
  • - Research Article

Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator

Huo Tang | H. M. Srivastava | ... | Li-Na Ma
  • Special Issue
  • - Volume 2014
  • - Article ID 251265
  • - Research Article

Differential Subordinations for Nonanalytic Functions

Georgia Irina Oros | Gheorghe Oros
  • Special Issue
  • - Volume 2014
  • - Article ID 603180
  • - Research Article

Upper Bound of Second Hankel Determinant for Certain Subclasses of Analytic Functions

Ming-Sheng Liu | Jun-Feng Xu | Ming Yang
  • Special Issue
  • - Volume 2014
  • - Article ID 467929
  • - Research Article

On Certain Subclass of Harmonic Starlike Functions

A. Y. Lashin
  • Special Issue
  • - Volume 2014
  • - Article ID 640856
  • - Research Article

Initial Coefficients of Biunivalent Functions

See Keong Lee | V. Ravichandran | Shamani Supramaniam
  • Special Issue
  • - Volume 2014
  • - Article ID 723097
  • - Research Article

Starlikeness of Functions Defined by Third-Order Differential Inequalities and Integral Operators

R. Chandrashekar | Rosihan M. Ali | ... | A. Swaminathan
  • Special Issue
  • - Volume 2014
  • - Article ID 476061
  • - Research Article

A Family of Minimal Surfaces and Univalent Planar Harmonic Mappings

Michael Dorff | Stacey Muir
Abstract and Applied Analysis
 Journal metrics
Acceptance rate14%
Submission to final decision40 days
Acceptance to publication54 days
CiteScore1.300
Impact Factor-
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