Themistocles M. Rassias
Encyclopedia
Themistocles M. Rassias is a Greek
mathematician
, and a professor at the National Technical University of Athens
(Eθνικό Μετσόβιο Πολυτεχνείο), Greece
. He has published more than 220 papers, 6 research books and 30 edited volumes in research Mathematics
as well as 4 textbooks in Mathematics (in Greek) for university students. His research work has received a large number of citations by several mathematicians. He serves as a member of the
Editorial Board
of several mathematical journals.
in Mathematics
from the University of California at Berkeley in June 1976. Professor Stephen Smale
and Professor Shiing-Shen Chern
have been his thesis and
academic advisors, respectively.
, Nonlinear Functional Analysis
, Approximation Theory
, Functional Equations, Inequalities, Metric Geometry and their Applications.
He has contributed a number of results in the stability of minimal submanifolds, in the solution of Ulam's Problem for approximate homomorphism
s in Banach spaces, in the theory of isometric mappings in metric space
s and in Complex analysis
(Poincare's inequality and harmonic mappings).
:
(i) Hyers–Ulam–Rassias stability
of functional equations.
(ii) The Aleksandrov–Rassias problem
for isometric mappings.
Greeks
The Greeks, also known as the Hellenes , are a nation and ethnic group native to Greece, Cyprus and neighboring regions. They also form a significant diaspora, with Greek communities established around the world....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, and a professor at the National Technical University of Athens
National Technical University of Athens
The National Technical University of Athens , sometimes simply known as Athens Polytechnic, is among the oldest and most prestigious higher education institutions of Greece....
(Eθνικό Μετσόβιο Πολυτεχνείο), Greece
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....
. He has published more than 220 papers, 6 research books and 30 edited volumes in research Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
as well as 4 textbooks in Mathematics (in Greek) for university students. His research work has received a large number of citations by several mathematicians. He serves as a member of the
Editorial Board
Editorial board
The editorial board is a group of people, usually at a publication, who dictate the tone and direction the publication's editorial policy will take.- Board makeup :...
of several mathematical journals.
Education
He received his Ph.D.Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
from the University of California at Berkeley in June 1976. Professor Stephen Smale
Stephen Smale
Steven Smale a.k.a. Steve Smale, Stephen Smale is an American mathematician from Flint, Michigan. He was awarded the Fields Medal in 1966, and spent more than three decades on the mathematics faculty of the University of California, Berkeley .-Education and career:He entered the University of...
and Professor Shiing-Shen Chern
Shiing-Shen Chern
Shiing-Shen Chern was a Chinese American mathematician, one of the leaders in differential geometry of the twentieth century.-Early years in China:...
have been his thesis and
academic advisors, respectively.
Research
His work extends over several fields of Mathematical Analysis. It includes Global Analysis, Analysis on Manifolds, Calculus of VariationsCalculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...
, Nonlinear Functional Analysis
Nonlinear functional analysis
Nonlinear functional analysis is a branch of Mathematical Analysis. It deals with nonlinear mappings and its subject matter includes:* generalizations of calculus to Banach spaces* implicit function theorems...
, Approximation Theory
Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby...
, Functional Equations, Inequalities, Metric Geometry and their Applications.
He has contributed a number of results in the stability of minimal submanifolds, in the solution of Ulam's Problem for approximate homomorphism
Homomorphism
In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures . The word homomorphism comes from the Greek language: ὁμός meaning "same" and μορφή meaning "shape".- Definition :The definition of homomorphism depends on the type of algebraic structure under...
s in Banach spaces, in the theory of isometric mappings in metric space
Metric space
In mathematics, a metric space is a set where a notion of distance between elements of the set is defined.The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space...
s and in Complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
(Poincare's inequality and harmonic mappings).
Mathematical Terminology
Some of his research work has been established with the scientific terminologyScientific terminology
While studying nature, scientists often encounter or create new material or immaterial objects and concepts and are compelled to name them. Most of those names are known only to professionals. However, due to popularization of science, they gradually become part of common languages...
:
(i) Hyers–Ulam–Rassias stability
Hyers–Ulam–Rassias stability
The stability problem of functional equations originated from a question of Stanislaw Ulam, posed in 1940, concerning the stability of group homomorphisms. In the next year, Donald H. Hyers gave a partial affirmative answer to the question of Ulam in the context of Banach spaces, that was the first...
of functional equations.
(ii) The Aleksandrov–Rassias problem
Aleksandrov–Rassias problem
The theory of isometries in the framework of Banach spaces has its beginning in a paper by Stanisław Mazur and Stanisław M. Ulam in 1932. They proved that each isometry of a normed real linear space onto a normed real linear space is a linear mapping up to translation...
for isometric mappings.
Awards and honors
He has received a number of honors and awards including:- 1977–1978 and 1978–1979, Membership offer from the School of Mathematics of the Institute for Advanced StudyInstitute for Advanced StudyThe Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in PrincetonPrinceton, New JerseyPrinceton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
, that he could not accept for family reasons. - 1980, Research AssociateResearch associateThe title of research associate is used to denote an academic research position at a university or similar institution. A research associate usually conducts research under the supervision of a principal investigator. In contrast to a research assistant or research officer, a research associate...
at the Department of Mathematics of Harvard UniversityHarvard UniversityHarvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
, invited by Raoul BottRaoul BottRaoul Bott, FRS was a Hungarian mathematician known for numerous basic contributions to geometry in its broad sense...
. - 1980, Visiting Research Professor at the Department of Mathematics of the Massachusetts Institute of TechnologyMassachusetts Institute of TechnologyThe Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
, invited by F. P. Peterson. - 1985–1986, 1986–1987, Teacher of the Year.
- 1987, Accademico Ordinario of the Accademia Tiberina, Roma.
- 1989–1990, 1990–1991, 1991–1992, Outstanding Faculty Member, University of La Verne, California (Athens Campus).
- 1991, FellowFellowA fellow in the broadest sense is someone who is an equal or a comrade. The term fellow is also used to describe a person, particularly by those in the upper social classes. It is most often used in an academic context: a fellow is often part of an elite group of learned people who are awarded...
of the Royal Astronomical SocietyRoyal Astronomical SocietyThe Royal Astronomical Society is a learned society that began as the Astronomical Society of London in 1820 to support astronomical research . It became the Royal Astronomical Society in 1831 on receiving its Royal Charter from William IV...
of London. - 2003, A volume entitled Stability of Functional Equations of Ulam-Hyers-Rassias Type was dedicated to the 25 years since the publication of Th. M. Rassias' Theorem, edited by S. Czerwik, Hadronic Press Inc., Florida.
- 2007, A special volume of the Banach Journal of Math. Analysis (Vol. 1, Issues 1 & 2) was dedicated to the 30th Anniversary of Th. M. Rassias' Stability Theorem.
- 2008, Doctor Honoris Causa (DHC), University of Alba Iulia (Romania).
- 2009, Α special issue of the Journal Nonlinear Functional Analysis and Applications (Vol.14, No.5) was dedicated to the 30th Anniversary of Th. M. Rassias' Stability Theorem.
- 2010, Ulam Prize in Mathematics.
- 2010, Honorary Doctorate, University of NisUniversity of NišThe University of Niš is a university located in Niš, Serbia. It was founded in 1965 and it consists of 13 faculties with 1500 teachers, 630 staff and extracurricular staff, and around 30,000 students...
(Serbia). - 2011, Α special issue of the Journal Nonlinear Sciences and Applications is dedicated to the 60th Anniversary of Th. M. Rassias' birth.
- 2011, A volume entitled Nonlinear Analysis: Stability, Approximation and Inequalities is dedicated to the 60th Anniversary of Th. M. Rassias' birth. (To be published by SpringerSpringer Science+Business Media- Selected publications :* Encyclopaedia of Mathematics* Ergebnisse der Mathematik und ihrer Grenzgebiete * Graduate Texts in Mathematics * Grothendieck's Séminaire de géométrie algébrique...
, New York, 2011).
See also
- Hyers-Ulam-Rassias stability, in: Encyclopaedia of Mathematics, Supplement III Hazewinkel, M. (ed.), Kluwer (2001) ISBN 1-4020-0198-3, pp. 194–196.
- Ulam-Hyers-Rassias Stability of Functional Equations, in: S. Czerwik, Functional Equations and Inequalities in Several Variables (Part II, pp. 129–260).