Functional equations in mathematical analysis

767 Pages·2012·3.326 MB·English

by  Themistocles M Rassias, Janusz Brzdȩk, SpringerLink (Online service) (eds.)

Springer Optimization and Its Applications
VOLUME52
ManagingEditor
PanosM.Pardalos(UniversityofFlorida)
Editor–CombinatorialOptimization
Ding-ZhuDu(UniversityofTexasatDallas)
AdvisoryBoard
J.Birge(UniversityofChicago)
C.A.Floudas(PrincetonUniversity)
F.Giannessi(UniversityofPisa)
H.D.Sherali(VirginiaPolytechnicandStateUniversity)
T.Terlaky(McMasterUniversity)
Y.Ye(StanfordUniversity)
AimsandScope
Optimization has been expanding in all directions at an astonishing rate
during the last few decades. New algorithmic and theoretical techniques
havebeendeveloped,thediffusionintootherdisciplineshasproceededata
rapidpace,andourknowledgeofallaspectsofthefieldhasgrownevenmore
profound.Atthe sametime, oneofthe moststriking trendsin optimization
is the constantly increasing emphasis on the interdisciplinary nature of the
field.Optimizationhasbeenabasictoolinallareasofappliedmathematics,
engineering,medicine,economicsandothersciences.
The series Springer Optimization and Its Applications publishes under-
graduate and graduate textbooks, monographs and state-of-the-art exposi-
tory works that focus on algorithms for solving optimization problems and
alsostudyapplicationsinvolvingsuchproblems.Someofthetopicscovered
include nonlinear optimization (convex and nonconvex), network flow
problems, stochastic optimization, optimal control, discrete optimization,
multi-objectiveprogramming,descriptionofsoftwarepackages,approxima-
tiontechniquesandheuristicapproaches.
Forfurthervolumes:
http://www.springer.com/series/7393

Themistocles M. Rassias • Janusz Brzde¸k
Editors
Functional Equations in
Mathematical Analysis
123
Editors
ThemistoclesM.Rassias JanuszBrzde¸k
DepartmentofMathematics DepartmentofMathematics
NationalTechnicalUniversityofAthens PedagogicalUniversity
ZografouCampus 30084Krakow
15780Athens Poland
Greece [email protected]
[email protected]
ISSN1931-6828
ISBN978-1-4614-0054-7 e-ISBN978-1-4614-0055-4
DOI10.1007/978-1-4614-0055-4
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2011935375
MathematicsSubjectClassification(2010):39-XX,46-XX,33-XX
©SpringerScience+BusinessMedia,LLC2012
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
NY10013, USA),except forbrief excerpts inconnection with reviews orscholarly analysis. Usein
connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,
orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.
Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare
notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject
toproprietaryrights.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Dedicatedtothememoryof
StanisławMarcin Ulam(1909–1984)
ontheoccasionofthe100thanniversary
ofhisbirth

Preface
Thevolumeconsistsofarticleswrittenbyeminentscientistsfromtheinternational
mathematical community, who present important research works in the field of
MathematicalAnalysisand relatedsubjects, in particular,in FunctionalEquations
andInequalities.Theseworksprovideaninsightinaprogressinthestudyofvarious
problemsofnonlinearcharacter.
Several of these results have been influenced by the work of the well-known
mathematician and physicist Stanisław Marcin Ulam (April 3, 1909 to May 13,
1984). An emphasis is given to one of his questions concerning approximate
homomorphisms.
The book is dedicated to the memory of Ulam on the occasion of the 100th
anniversaryofhisbirth.
Itisdividedintotwoparts.PartIfocusesonseveralaspectsoftheUlamstability
theory.PartIIcontainspapersonvarioussubjectsofMathematicalAnalysis.
Itis a pleasureto expressourdeepestthankstoall ofthe mathematicianswho,
throughtheirworks,participatedinthisvolume.
We would also wish to acknowledge the superb assistance that the staff of
Springerhasprovidedinthepreparationofthispublication.
AthensandCracow ThemistoclesM.Rassias
JanuszBrzde¸k
vii

Contents
PartI StabilityinMathematicalAnalysis
1 StabilityPropertiesofSomeFunctionalEquations..................... 3
RomanBadora
2 NoteonSuperstabilityofMikusin´ski’sFunctionalEquation.......... 15
BogdanBatko
3 A General Fixed Point Method for the Stability
ofCauchyFunctionalEquation........................................... 19
LiviuCa˘dariuandViorelRadu
4 OrthogonalityPreservingPropertyanditsUlamStability............ 33
JacekChmielin´ski
5 OntheHyers–UlamStabilityofFunctionalEquations
withRespecttoBoundedDistributions .................................. 59
Jae-YoungChung
6 StabilityofMulti-JensenMappingsinNon-Archimedean
NormedSpaces.............................................................. 79
KrzysztofCieplin´ski
7 OnStabilityoftheEquationofHomogeneousFunctions
onTopologicalSpaces...................................................... 87
StefanCzerwik
8 Hyers–UlamStabilityoftheQuadraticFunctionalEquation......... 97
ElhoucienElqorachi,YoussefManar,
andThemistoclesM.Rassias
9 IntuitionisticFuzzyApproximatelyAdditiveMappings ............... 107
M.Eshaghi-Gordji,H.Khodaei,H.Baghani,
andM.Ramezani
ix