Table Of ContentJanusz Brzdęk · Dorian Popa
Themistocles M. Rassias Editors
Ulam Type
Stability
Ulam Type Stability
˛
Janusz Brzdek • Dorian Popa
Themistocles M. Rassias
Editors
Ulam Type Stability
123
Editors
JanuszBrzde˛k DorianPopa
DepartmentofAppliedMathematics DepartmentofMathematics
AGHUniversityofScienceandTechnology TechnicalUniversityofCluj-Napoca
Krakow,Poland Cluj-Napoca,Romania
ThemistoclesM.Rassias
DepartmentofMathematics
NationalTechnicalUniversityofAthens
Athens,Greece
ISBN978-3-030-28971-3 ISBN978-3-030-28972-0 (eBook)
https://doi.org/10.1007/978-3-030-28972-0
Mathematics Subject Classification (2010): 06B99, 20M99, 30D05, 30E25, 34D10, 37C25, 39A30,
39B12,39B22,39B32,39B52,39B62,39B82,43A22,45M10,46B20,47H10,47H14,47J20,47L05,
54H25,60K25,65J15,65Q20,91B32,91B38
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Preface
Thisvolumepresentspaperswrittenbyexperts,whoareactivelyworkinginvarious
areasofmathematicsanditsapplicationsonissuesinonewayoranotherconnected
to Ulam-type stability problems, motivated by the famous question concerning
approximate homomorphisms. These papers provide an insightful perspective on
alargenumberofinvestigationsinmathematicalanalysis.
The present book is the outcome of two Conferences on Ulam Type Stability
(CUTS)organizedin2016(July4–9,Cluj-Napoca,Romania)andin2018(October
8–13,Timis¸oara,Romania).
The aim of the volume is not only to give an account of the present state of
research on Ulam-type stability but also to stimulate further research in the area.
Thus, alongside research papers containing new results, it includes surveys on
various themes pointing to the potential for further future study and identifying
severalopenproblemsand/orquestions.
Let us recall that S.M. Ulam (April 13, 1909–May 13, 1984) was a prominent
mathematician and physicist. In 1940, he posed his famous question concerning
approximate homomorphisms, which gave rise to a long-lasting study of a field
whichwenowcallUlam(orHyers-Ulam)stability.
The book contains 21 articles written by 29 authors from 12 countries, all
of whom have been intensively involved in active research in this area. Special
emphasis has been placed on the topics which apply methods and techniques
involving,ororiginatingfrom,functionalequationsandinequalities(FEI).
Wehopethatthispublicationwillserveasakindofguidebookforbothgraduate
studentsandresearchersinvariousfields,includingnotonlymathematicsbutalso
physics,engineering,andinterdisciplinaryresearch.
Subjects treated in this book are (in order of appearance in this volume) as
follows:
– StabilityandsolutionsoftheCauchyfunctionalequationinlatticeenvironments
– Fixed-pointapproachtotheHyers-Ulamstabilityandhyperstabilityofageneral
functionalequation
– ReversingpropertyoftheBirkhoff-Jamesorthogonalityanditsstability
v
vi Preface
– Optimal forward contract design for inventory (a value-of-waiting analysis via
sensitivityanalysisofafunctionalequation)
– Hyers-Ulamstabilityoffunctionalequationsinquasi-β-Banachspaces
– Stability of the functional equation of p-Wright affine functions in 2-Banach
spaces
– Solutionsandstabilityofafunctionalequationarisingfromaqueueingsystem
– Approximatelycubicmappings
– Solutionsandstabilityofsomefunctionalequationsonsemigroups
– Bi-additive s-functional inequalities and quasi-∗-multipliers on Banach ∗-
algebras
– Ulam stability of a generalization of the Fréchet functional equation on a
restricteddomain
– Variousremarksconcerningthenotionofstabilityoffunctionalequations
– Subdominanteigenvaluelocationofabordereddiagonalmatrix
– Afixed-pointtheoreminuniformizablespaces
– SymmetryofBirkhoff-Jamesorthogonalityofboundedlinearoperators
– Ulamstabilityofzero-pointequations
– CauchydifferenceoperatorinsomeOrliczspaces
– Semi-innerproductsandparapreseminormsongroupsandageneralizationofa
theoremofMaksaandVolkmannonadditivefunctions
– InvariantmeansinUlam-typestabilitytheory
– GeometryofBanachfunctionmodules
– Exactandapproximateorthogonalitiesbasedonnormderivatives
It is our pleasure to express warmest thanks to all the mathematicians, who
participated in this publication. We would also wish to acknowledge the support
ofourreferees.
Lastbutnotleast,wewishtoacknowledgethesuperbassistancethatthestaffof
Springerprovidedforthepublicationofthisvolume.
Krakow,Poland JanuszBrzde¸k
Cluj-Napoca,Romania DorianPopa
Athens,Greece ThemistoclesM.Rassias
March2019
Contents
1 SurveyonCauchyFunctionalEquationinLatticeEnvironments.... 1
NutefeKwamiAgbeko
2 APurelyFixedPointApproachtotheUlam-HyersStability
andHyperstabilityofaGeneralFunctionalEquation ................. 47
ChaimaaBenzaroualaandLahbibOubbi
3 Birkhoff–JamesOrthogonalityReversingProperty
andItsStability............................................................. 57
JacekChmielin´skiandPawełWójcik
4 OptimalForwardContractDesignforInventory:
AValue-of-WaitingAnalysis .............................................. 73
RoyO.DaviesandAdamJ.Ostaszewski
5 Ulam-HyersStabilityofFunctionalEquations
inQuasi-β-BanachSpaces................................................. 97
NguyenVanDungandWutipholSintunavarat
6 OnStabilityoftheFunctionalEquationofp-WrightAffine
Functionsin2-BanachSpaces............................................. 131
El-SayedEl-hady
7 OnSolutionsandStabilityofaFunctionalEquationArising
fromaQueueingSystem................................................... 143
El-SayedEl-hady
8 ApproximationbyCubicMappings...................................... 153
Pas¸cGa˘vru¸taandLauraManolescu
9 SolutionsandStabilityofSomeFunctionalEquations
onSemigroups .............................................................. 167
KeltoumaBelfakih,ElhoucienElqorachi,
andThemistoclesM.Rassias
vii
viii Contents
10 Bi-additives-FunctionalInequalitiesandQuasi-∗-Multipliers
onBanach∗-Algebras...................................................... 199
JungRyeLee,ChoonkilPark,andThemistoclesM.Rassias
11 OnUlamStabilityofaGeneralizationoftheFréchetFunctional
EquationonaRestrictedDomain ........................................ 217
RenataMalejki
12 MiscellaneaAbouttheStabilityofFunctionalEquations.............. 231
ZenonMoszner
13 SubdominantEigenvalueLocationandtheRobustness
ofDividendPolicyIrrelevance ............................................ 273
AdamJ.Ostaszewski
14 AFixedPointTheoreminUniformizableSpaces....................... 325
LahbibOubbi
15 Symmetry of Birkhoff-James Orthogonality of Bounded
LinearOperators........................................................... 331
KallolPaul,DebmalyaSain,andPujaGhosh
16 UlamStabilityofZeroPointEquations.................................. 345
AdrianPetrus¸elandIoanA.Rus
17 CauchyDifferenceOperatorinSomeOrliczSpaces ................... 365
StanisławSiudut
18 Semi-InnerProductsandParapreseminormsonGroupsand
aGeneralizationofaTheoremofMaksaandVolkmannon
AdditiveFunctions ......................................................... 383
ÁrpádSzáz
19 InvariantMeansinStabilityTheory ..................................... 409
LászlóSzékelyhidi
20 OnGeometryofBanachFunctionModules:SelectedTopics ......... 453
PawełWójcik
21 OnExactandApproximateOrthogonalitiesBasedonNorm
Derivatives................................................................... 469
AliZamaniandMahdiDehghani
Index............................................................................... 509
Contributors
NutefeKwamiAgbeko InstituteofMathematics,UniversityofMiskolc,Miskolc,
Hungary
Keltouma Belfakih Department of Mathematics, Faculty of Sciences, University
IbnZohr,Agadir,Morocco
Jacek Chmielin´ski Department of Mathematics, Pedagogical University of
Cracow,Kraków,Poland
Roy O. Davies School of Mathematics and Actuarial Science, University of
Leicester,Leicester,UK
Mahdi Dehghani Department of Pure Mathematics, Faculty of Mathematical
Sciences,UniversityofKashan,Kashan,Iran
Nguyen Van Dung Faculty of Mathematics Teacher Education, Dong Thap
University,CaoLanh,DongThap,Vietnam
El-SayedEl-hady MathematicsDepartment,CollegeofScience,JoufUniversity,
Sakaka,KingdomofSaudiArabia
Basic Science Department, Faculty of Computers and Informatics, Suez Canal
University,Ismailia,Egypt
ElhoucienElqorachi DepartmentofMathematics,FacultyofSciences,University
IbnZohr,Agadir,Morocco
Pas¸c Ga˘vrut¸a Department of Mathematics, Politehnica University of Timis¸oara,
Timis¸oara,Romania
Puja Ghosh Department of Mathematics, Sabang Sajanikanta Mahavidyalaya,
PaschimMedinipur,WestBengal,India
JungRyeLee DaejinUniversity,Pocheon-si,SouthKorea
ix
x Contributors
Renata Malejki Institute of Mathematics, Pedagogical University of Cracow,
Kraków,Poland
Laura Manolescu Department of Mathematics, Politehnica University of Tim-
is¸oara,Timis¸oara,Romania
Zenon Moszner Institute of Mathematics, Pedagogical University of Cracow,
Kraków,Poland
AdamJ.Ostaszewski DepartmentofMathematics,LondonSchoolofEconomics,
London,UK
Lahbib Oubbi Department of Mathematics, Team GrAAF, Laboratory LMSA,
Center CeReMar, Ecole Normale Supérieure, Mohammed V University in Rabat,
Takaddoum,Rabat,Morocco
ChoonkilPark HanyangUniversity,Seoul,SouthKorea
KallolPaul DepartmentofMathematics,JadavpurUniversity,Kolkata,India
AdrianPetrus¸el Babes¸-BolyaiUniversity,Cluj-Napoca,Romania
AcademyofRomanianScientists,Bucharest,Romania
Themistocles M. Rassias Department of Mathematics, National Technical
UniversityofAthens,Athens,Greece
IoanA.Rus Babes¸-BolyaiUniversity,Cluj-Napoca,Romania
Debmalya Sain Department of Mathematics, Indian Institute of Science,
Bangalore,India
Wutiphol Sintunavarat Department of Mathematics and Statistics, Faculty of
Science and Technology, Thammasat University Rangsit Center, Pathumthani,
Thailand
Stanisław Siudut Institute of Mathematics, Pedagogical University, Kraków,
Poland
Árpád Száz Department of Mathematics, University of Debrecen, Debrecen,
Hungary
László Székelyhidi Institute of Mathematics, University of Debrecen, Debrecen,
Hungary
Paweł Wójcik Department of Mathematics, Pedagogical University of Cracow,
Kraków,Poland
AliZamani DepartmentofMathematics,FarhangianUniversity,Tehran,Iran
Chaimaa BenZarouala Department of Mathematics, Team GrAAF, Laboratory
LMSA,CenterCeReMar,FacultyofSciences,MohammedVUniversityinRabat,
Rabat,Morocco
