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Janusz 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 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland 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
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