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Springer Optimization and Its Applications 154 Themistocles M. Rassias Panos M. Pardalos Editors Mathematical Analysis and Applications Springer Optimization and Its Applications Volume 154 ManagingEditor PanosM.Pardalos (UniversityofFlorida) MyT.Thai(UniversityofFlorida) Editor-CombinatorialOptimization Ding-ZhuDu(UniversityofTexasatDallas) AdvisoryBoard J.Birge(UniversityofChicago) S.Butenko(TexasA&MUniversity) F.Giannessi(UniversityofPisa) S.Rebennack(KarlsruheInstituteofTechnology) T.Terlaky(LehighUniversity) Y.Ye(StanfordUniversity) AimsandScope Optimizationhascontinuedtoexpandinalldirectionsatanastonishingrate.New algorithmicandtheoreticaltechniquesarecontinuallydevelopingandthediffusion into other disciplines is proceeding at a rapid pace, with a spot light on machine learning, artificial intelligence, and quantum computing. Our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in areas not limited to applied mathematics, engineering, medicine, economics, computer science,operationsresearch,andothersciences. The series Springer Optimization and Its Applications (SOIA) aims to publish state-of-the-art expository works (monographs, contributed volumes, textbooks, handbooks)thatfocusontheory,methods,andapplicationsofoptimization.Topics coveredinclude,butarenotlimitedto,nonlinearoptimization,combinatorialoptimization,continuousoptimization,stochasticoptimization,Bayesianoptimization, optimalcontrol,discreteoptimization,multi-objectiveoptimization,andmore.New totheseriesportfolioincludeWorksattheintersectionofoptimizationandmachine learning,artificialintelligence,andquantumcomputing. VolumesfromthisseriesareindexedbyWebofScience,zbMATH,Mathematical Reviews,andSCOPUS. Moreinformationaboutthisseriesathttp://www.springer.com/series/7393 Themistocles M. Rassias • Panos M. Pardalos Editors Mathematical Analysis and Applications 123 Editors ThemistoclesM.Rassias PanosM.Pardalos DepartmentofMathematics DepartmentofIndustrial ZografouCampus andSystemsEngineering NationalTechnicalUniversityofAthens UniversityofFlorida Athens,Greece Gainesville,FL,USA ISSN1931-6828 ISSN1931-6836 (electronic) SpringerOptimizationandItsApplications ISBN978-3-030-31338-8 ISBN978-3-030-31339-5 (eBook) https://doi.org/10.1007/978-3-030-31339-5 MathematicsSubjectClassification:26-XX,28-XX,30-XX,32-XX,35-XX,91-XX ©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 Mathematical Analysis and Applications is devoted to the presentation of high- quality research and survey papers belonging to a broad spectrum of areas in which Analysis plays a central role. The book in hand provides an insight into the investigation of several problems and theories in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, Radon transform, nonlinear analysis, and various applications of interdisciplinary research.Thecontributingpapershavebeenwrittenbyeminentscientistsfromthe internationalmathematicalcommunitywhoareexpertsintheindividualsubjects. In this book, some papers are devoted to certain applications as for example in the three-body problem, finite element analysis in fluid mechanics, algorithms for differenceofmonotoneoperators,avibrationalapproachtoafinancialproblem,etc. Thispublicationprovidesvaluableandup-to-dateinformationaswellasresearch results which are hoped to be useful to graduate students and researchers working inMathematics,Physics,Engineering,andEconomics. Itisourpleasuretoexpressourthankstoallthecontributorsofchaptersinthis bookwhoparticipatedinthiscollectiveeffort. Last but not least, we would like to acknowledge the superb assistance that the staffofSpringerhasprovidedforthepublicationofthiswork. Athens,Greece ThemistoclesM.Rassias Gainesville,FL,USA PanosM.Pardalos v Contents Exact Solution to Systems of Linear First-Order Integro-DifferentialEquationswithMultipoint andIntegralConditions ......................................................... 1 M.M.BaiburinandE.Providas AVariationalApproachtotheFinancialProblemwithInsolvencies andAnalysisoftheContagion.................................................. 17 GiorgiaCappello,PatriziaDaniele,SofiaGiuffrè,andAntoninoMaugeri FixedPointTheoremsforaSystemofMappingsinGeneralized b-MetricSpaces .................................................................. 41 StefanCzerwikandThemistoclesM.Rassias InequalitiesandApproximationsfortheFiniteHilbertTransform: ASurveyofRecentResults ..................................................... 53 SilvestruSeverDragomir OnHyperstabilityoftheTwo-VariableJensenFunctionalEquation onRestrictedDomain............................................................ 165 Iz-iddineEL-Fassi On the Study of Circuit Chains Associated with a Random Walk with Jumps in Fixed, Random Environments: Criteria ofRecurrenceandTransience.................................................. 185 ChrysoulaGanatsiou OnSelectionsofSomeGeneralizedSet-ValuedInclusions.................. 205 BahmanHayati,HamidKhodaei,andThemistoclesM.Rassias CertainFractionalIntegralandDifferentialFormulasInvolving theExtendedIncompleteGeneralizedHypergeometricFunctions......... 217 PraveenAgarwal,ThemistoclesM.Rassias,GurmejSingh, andShilpiJain vii viii Contents OntheStabilityoftheTriangularEquilibriumPointsintheElliptic RestrictedThree-BodyProblemwithRadiationandOblateness........... 273 VassilisS.Kalantonis,AngelaE.Perdiou,andEfstathiosA.Perdios SomeDifferentTypeIntegralInequalitiesandTheirApplications ........ 287 ArtionKashuriandRozanaLiko ExtensionsofKannappan’sandVanVleck’sFunctionalEquations onSemigroups.................................................................... 319 KeltoumaBelfakih,ElhoucienElqorachi,andAhmedRedouani RecentAdvancesofConvexityTheoryandItsInequalities................. 339 JichangC.Kuang AdditiveFunctionalInequalitiesandPartialMultipliersinComplex BanachAlgebras ................................................................. 365 JungRyeLee,ChoonkilPark,andThemistoclesM.Rassias Additiveρ-FunctionalInequalitiesandTheirApplications................. 391 Jung Rye Lee, Choonkil Park, Themistocles M. Rassias, andXiaohongZhang GraphicContractionPrincipleandApplications ............................ 411 A.Petrus¸elandI.A.Rus ANewApproachfortheInversionoftheAttenuated RadonTransform ................................................................ 433 NicholasE.Protonotarios,GeorgeA.KastisandAthanassiosS.Fokas OnAlgorithmsforDifferenceofMonotoneOperators...................... 459 MaedeRamazannejad,MohsenAlimohammady,andCarloCattani FiniteElementAnalysisinFluidMechanics.................................. 481 AnastasiosRaptis,KonstantinaKyriakoudi,andMichailA.Xenos OnaHilbert-TypeIntegralInequalityintheWholePlaneRelated totheExtendedRiemannZetaFunction...................................... 511 MichaelTh.RassiasandBichengYang OnMetricStructuresofNormedGyrogroups................................ 529 TeerapongSuksumran Birelator Spaces Are Natural Generalizations of Not Only BitopologicalSpaces,ButAlsoIdealTopologicalSpaces.................... 543 ÁrpádSzáz PPFDependentFixedPointsinRazumikhinMetricalChains ............. 587 MihaiTurinici Contents ix Equivalent Properties of Parameterized Hilbert-Type Integral Inequalities........................................................................ 639 BichengYang TrotterProductFormulaforNon-self-AdjointGibbsSemigroups......... 677 ValentinA.Zagrebnov Exact Solution to Systems of Linear First-Order Integro-Differential Equations with Multipoint and Integral Conditions M.M.BaiburinandE.Providas Abstract Thispaperisdevotedtothestudyofnonhomogeneoussystemsoflinear first-orderordinaryintegro-differentialequationsofFredholmtypewithmultipoint and integral boundary constraints. Sufficient conditions for the solvability and correctness of the problem are established and the unique solution is provided in closed-form.Theapproachfollowedisbasedontheextensiontheoryofoperators. 1 Introduction Mathematicalmodelinginthetheoryofautomaticcontrol,thetheoryofoscillation, mathematical physics, biology, applied mathematics, and economics, very often, leadstothestudyofmultipointboundaryvalueproblemsfordifferential,functional- differential, and integro-differential equations. These types of boundary value problems and their solutions have been investigated by many researchers, for example, [1, 2, 5, 8, 9, 21]. Of special interest are the multipoint boundary value problemsforasystemofdifferentialequations(DEs)andintegro-differentialequa- tions(IDEs),see,forexample, [4,6,11,12,22].Itshouldbenotedthatobtaining exact solutions even to multipoint boundary value problems for a differential, or an integro-differential equation, is a difficult task. Therefore, usually numerical methodsareemployedasin[3,7,15]andelsewhere. Recently,in[6]thesolutiontoaclassofboundaryvalueproblemsforasystem of linear first-order DEs coupled with multipoint and integral conditions has been obtainedinclosed-form.Here,wecontinuethisstudytosystemsoflinearfirst-order M.M.Baiburin DepartmentofFundamentalMathematics,L.N.GumilyovEurasianNationalUniversity,Astana, RepublicofKazakhstan e-mail:[email protected] E.Providas((cid:2)) UniversityofThessaly,Larissa,Greece e-mail:[email protected] ©SpringerNatureSwitzerlandAG2019 1 T.M.Rassias,P.M.Pardalos(eds.),MathematicalAnalysis andApplications,SpringerOptimizationandItsApplications154, https://doi.org/10.1007/978-3-030-31339-5_1 2 M.M.BaiburinandE.Providas ordinaryIDEsofFredholmtypewithmultipointandintegralboundaryconstraints. The method proposed is based on the extension theory of linear operators in a Banach space, as it has been developed in terms of inverse operators [5, 13] and in terms of direct operators [14], and has been used to investigate the correctness properties to some extensions of operators [10, 16, 20] and more recently to solveexactlyinitialandtwo-pointboundaryvalueproblemsforintegro-differential equations[17–19]. We first examine the solvability conditions and then obtain the exact solution of the following system of IDEs subject to multipoint and integral boundary conditions: (cid:3) (cid:2)m 1 y(cid:2)(x)−Ay(x)− G (x) H (t)y(t)dt =f(x), x ∈[0,1], i i i=0 0 (cid:3) (cid:2)m (cid:2)s ξj+1 A y(x )+ B C (t)y(t)dt =0, (1) i i j j i=0 j=0 ξj whereA, A , B aren×nconstantmatrices,G (x), H (x), C (x)arevariablen× i j i i j nmatrices,whoseelementsarecontinuousfunctionson[0,1],f(x)isavectorofn continuousfunctionson[0,1],andy(x)isavectorofnsoughtcontinuousfunctions with continuous derivatives on [0,1]; the points x ,ξ satisfy the conditions 0 = i j x0 < x1 < ··· < xm−1 < xm = 1, 0 = ξ0 < ξ1 < ··· < ξs < ξs+1 = 1. The problem (1)maybeobtained asaperturbation ofacorresponding boundary value problemforasystemoffirst-orderDEs,specifically y(cid:2)(x)−Ay(x)=f(x), (cid:3) (cid:2)m (cid:2)s ξj+1 A y(x )+ B C (t)y(t)dt =0, (2) i i j j i=0 j=0 ξj whosesolvabilityandtheconstructionoftheexactsolutionwereinvestigatedin[6]. The rest of the paper is organized as follows. In Section 2 some necessary definitionsaregivenandpreliminaryresultsarederived.InSection3thetwomain theoremsfortheexistenceandtheconstructionoftheexactsolutionarepresented. Lastly,someconclusionsaredrawninSection4. 2 Definitionsand PreliminaryResults LetX,Y becomplexBanachspaces.LetP : X → Y denotealinearoperatorand D(P)andR(P)itsdomainandtherange,respectively.AnoperatorP iscalledan extension of the operator P : X → Y if D(P ) ⊆ D(P) and Pu = P u, for all 0 0 0 u∈D(P ).AnoperatorP :X →Y iscalledcorrectifR(P)=Y andtheinverse 0 operatorP−1 existsandiscontinuousonY.