Hindawi Publishing Corporation
Abstract and Applied Analysis
Volume 2013, Article ID 463493, 1 page
http://dx.doi.org/10.1155/2013/463493
Editorial
Trends in Classical Analysis, Geometric Function Theory,
and Geometry of Conformal Invariants
Árpád Baricz,1 Saminathan Ponnusamy,2 Matti Vuorinen,3 and Karl-Joachim Wirths4
1
Department of Economics, Babes-Bolyai University, Cluj-Napoca, Romania
Department of Mathematics and Statistics, Indian Institute of Technology Madras, Chennai 600036, India
3
Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland
4
Institut for Analysis and Algebra, TU Braunschweig, 38106 Braunschweig, Germany
2
Correspondence should be addressed to Saminathan Ponnusamy; samy@iitm.ac.in
Received 11 November 2012; Accepted 11 November 2012
Copyright © 2013 Árpád Baricz et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The present special issue of the Journal of Abstract and
Applied Analysis is devoted to trends in classical analysis, geometric function theory, and geometry of conformal mappings.
In the sense of the title of this journal, we wanted to
present a spectrum of research themes reaching from applied
analysis to pure analysis and from applications of analysis in
geometry to applications in differential equations and integral
equations.
Further, our aim was to find articles on classical function
theory as well as on its generalizations in several directions.
One additional aspect, that was paid attention to, is the
tendency of mathematics to use computers to solve problems
by new and effective algorithms. In detail, we addressed to the
following themes.
That we did not forget classical pure analysis is proved
by an article that considers harmonic functions on Riemann
manifolds and by an article on geometry and topology of
Banach spaces.
The classical geometric function theory is represented by
an article on univalence criterions associated with the nth
derivative.
The relationships between conformal mappings and integral equations are in the scope of two articles, where algorithms are proved to compute the mappings of unbounded
multiply connected as well as bounded multiply connected
regions onto slit regions.
Other old themes of classical function theory are entire
functions for which we publish a paper on uniqueness theorems for monomials of entire functions.
Concerning the generalizations of classical analysis, we
incorporated a paper on the stability of solutions of fractional
differential equations and two papers on harmonic mappings, specially one on the general theory of log-harmonic
mappings and one on certain classes of harmonic mappings
defined by convolutions.
The papers on the generalizations of holomorphic functions are completed by a longer article on the distribution
of zeros and poles of the rational approximants of a nonholomorphic function on an interval.
The aspect of new algorithms is addressed in an article
on Hermite interpolation using Möbius transformations of
planar Pythagorean-hodograph cubics and in a paper where
algorithms to calculate inverse Z-transforms on the unit disc
by number-theoretical methods are proved.
We hope that in this broad variety of analytic themes
many researchers can find something interesting and new.
Árpád Baricz
Saminathan Ponnusamy
Matti Vuorinen
Karl-Joachim Wirths
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