Special Issue "Symmetry in Geometric Functions and Mathematical Analysis"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics and Symmetry".

Deadline for manuscript submissions: 21 December 2020.

Special Issue Editors

Prof. Dr. Stanisława Kanas
Website
Guest Editor
Institute of Mathematics, University of Rzeszow, Poland
Interests: complex analysis and potential theory; partial differential equations; subordinations and complex operator theory; geometrical aspects of complex analysis; harmonic and quasiconformal mappings; generalized complex analysis; complex dynamical systems and fractals; entire and meromorphic functions; special functions; applications
Prof. Dr. Toshiyuki Sugawa

Guest Editor
Tohoku University
Interests: complex analysis and applications

Special Issue Information

Dear Colleagues,

This Special Issue “Symmetry in Geometric Functions and Mathematical Analysis” is devoted to the publication of high-quality research, especially relating to its geometrical aspects and harmonic and quasiconformal mappings (including applications in allied areas of mathematics and mathematical sciences). The issue will provide a forum for researchers and scientists to communicate their recent developments and to present recent results in the theory of complex analysis of one and several variables, and application in algebraic geometry, number theory, as well as in physics, including the branches of hydrodynamics and quantum mechanics.

The research topics include but are not limited to:

  1. Complex analysis and potential theory;
  2. Partial differential equations;
  3. Geometrical aspects of complex analysis;
  4. Complex approximation theory;
  5. Harmonic and quasiconformal mappings;
  6. Generalized complex analysis;
  7. Complex dynamical systems and fractals;
  8. Entire and meromorphic functions;
  9. Applications

Prof. Dr. Stanisława Kanas
Prof. Dr. Toshiyuki Sugawa
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • harmonic and quasiconformal mappings
  • entire and meromorphic functions
  • univalent and multivalent functions
  • subordinations and complex operator theory
  • geometrical aspects of complex analysis
  • special functions
  • applications of symmetry in mathematical analysis

Published Papers (6 papers)

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Research

Open AccessArticle
Estimates of Coefficient Functionals for Functions Convex in the Imaginary-Axis Direction
Symmetry 2020, 12(10), 1736; https://doi.org/10.3390/sym12101736 - 20 Oct 2020
Abstract
Let C0(h) be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula Re{(1z2)f(z)}>0. In this [...] Read more.
Let C0(h) be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula Re{(1z2)f(z)}>0. In this paper, some coefficient problems for C0(h) are considered. Some properties and bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates of the difference and of sum of successive coefficients, bounds of the sum of the first n coefficients and bounds of the n-th coefficient. The obtained results are used to determine coefficient estimates for both functions convex in the imaginary-axis direction with real coefficients and typically real functions. Moreover, the sum of the first initial coefficients for functions with a positive real part and with a fixed second coefficient is estimated. Full article
(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis)
Open AccessArticle
Some Results of Fekete-Szegö Type. Results for Some Holomorphic Functions of Several Complex Variables
Symmetry 2020, 12(10), 1707; https://doi.org/10.3390/sym12101707 - 16 Oct 2020
Abstract
This paper is devoted to a generalization of the well-known Fekete-Szegö type coefficients problem for holomorphic functions of a complex variable onto holomorphic functions of several variables. The considerations concern three families of such functions f, which are bounded, having positive real [...] Read more.
This paper is devoted to a generalization of the well-known Fekete-Szegö type coefficients problem for holomorphic functions of a complex variable onto holomorphic functions of several variables. The considerations concern three families of such functions f, which are bounded, having positive real part and which Temljakov transform Lf has positive real part, respectively. The main result arise some sharp estimates of the Minkowski balance of a combination of 2-homogeneous and the square of 1-homogeneous polynomials occurred in power series expansion of functions from aforementioned families. Full article
(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis)
Open AccessArticle
Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case
Symmetry 2020, 12(9), 1550; https://doi.org/10.3390/sym12091550 - 20 Sep 2020
Abstract
Scators form a vector space endowed with a non-distributive product, in the hyperbolic case, have physical applications related to some deformations of special relativity (breaking the Lorentz symmetry) while the elliptic case leads to new examples of hypercomplex numbers and related notions of [...] Read more.
Scators form a vector space endowed with a non-distributive product, in the hyperbolic case, have physical applications related to some deformations of special relativity (breaking the Lorentz symmetry) while the elliptic case leads to new examples of hypercomplex numbers and related notions of holomorphicity. Until now, only a few particular cases of scator holomorphic functions have been found. In this paper we obtain all solutions of the generalized Cauchy–Riemann system which describes analogues of holomorphic functions in the (1+2)-dimensional scator space. Full article
(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis)
Open AccessArticle
New Identities Dealing with Gauss Sums
Symmetry 2020, 12(9), 1416; https://doi.org/10.3390/sym12091416 - 26 Aug 2020
Abstract
In this article, we used the elementary methods and the properties of the classical Gauss sums to study the problem of calculating some Gauss sums. In particular, we obtain some interesting calculating formulas for the Gauss sums corresponding to the eight-order and twelve-order [...] Read more.
In this article, we used the elementary methods and the properties of the classical Gauss sums to study the problem of calculating some Gauss sums. In particular, we obtain some interesting calculating formulas for the Gauss sums corresponding to the eight-order and twelve-order characters modulo p, where p be an odd prime with p=8k+1 or p=12k+1. Full article
(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis)
Open AccessArticle
The Fifth Coefficient of Bazilevič Functions
Symmetry 2020, 12(8), 1228; https://doi.org/10.3390/sym12081228 - 26 Jul 2020
Abstract
Let fA, the class of normalized analytic functions defined in the unit disk D, and be given by f(z)=z+n=2anzn for zD. [...] Read more.
Let fA, the class of normalized analytic functions defined in the unit disk D, and be given by f(z)=z+n=2anzn for zD. This paper presents a new approach to finding bounds for |an|. As an application, we find the sharp bound for |a5| for the class B1(α) of Bazilevič functions when α1. Full article
(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis)
Open AccessArticle
Subclasses of Starlike and Convex Functions Associated with the Limaçon Domain
Symmetry 2020, 12(6), 942; https://doi.org/10.3390/sym12060942 - 03 Jun 2020
Cited by 2
Abstract
Let STL(s) and CVL(s) denote the family of analytic and normalized functions f in the unit disk D:=z:|z|<1, such that the quantity zf [...] Read more.
Let ST L ( s ) and CV L ( s ) denote the family of analytic and normalized functions f in the unit disk D : = z : | z | < 1 , such that the quantity z f ( z ) / f ( z ) or 1 + z f ( z ) / f ( z ) respectively are lying in the region bounded by the limaçon ( u 1 ) 2 + v 2 s 4 2 = 4 s 2 u 1 + s 2 2 + v 2 , where 0 < s 1 / 2 . The limaçon of Pascal is a curve that possesses properties which qualify it for the several applications in mathematics, statistics (hypothesis testing problem) but also in mechanics (fluid processing applications, known limaçon technology is employed to extract electrical power from low-grade heat, etc.). In this paper we present some results concerning the behavior of f on the classes ST L ( s ) or CV L ( s ) . Some appropriate examples are given. Full article
(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis)
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