Handbook of functional equations. Functional inequalities

555 Pages·2014·2.75 MB·English

by  Themistocles M. Rassias (ed.)

Springer Optimization and Its Applications
Volume 95
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
Optimizationhasbeenexpandinginalldirectionsatanastonishingrateduringthe
lastfewdecades.Newalgorithmicandtheoreticaltechniqueshavebeendeveloped,
thediffusionintootherdisciplineshasproceededatarapidpace,andourknowledge
ofallaspectsofthefieldhasgrownevenmoreprofound.Atthesametime,oneof
themoststrikingtrendsinoptimizationistheconstantlyincreasingemphasisonthe
interdisciplinarynatureofthefield. Optimizationhasbeenabasictoolinallareas
ofappliedmathematics,engineering,medicine,economics,andothersciences.
The series Springer Optimization and ItsApplications publishes undergraduate
and graduate textbooks, monographs and state-of-the-art expository work that fo-
cus on algorithms for solving optimization problems and also study applications
involvingsuchproblems.Someofthetopicscoveredincludenonlinearoptimization
(convex and nonconvex), network flow problems, stochastic optimization, optimal
control,discreteoptimization,multi-objectiveprogramming,descriptionofsoftware
packages,approximationtechniquesandheuristicapproaches.
Moreinformationaboutthisseriesathttp://www.springer.com/series/7393
Themistocles M. Rassias
Editor
Handbook of Functional
Equations
Functional Inequalities
2123
Editor
ThemistoclesM.Rassias
DepartmentofMathematics
NationalTechnicalUniversityofAthens
Athens,Greece
ISSN1931-6828 ISSN1931-6836(electronic)
ISBN978-1-4939-1245-2 ISBN978-1-4939-1246-9(eBook)
DOI10.1007/978-1-4939-1246-9
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2014949795
MathematicsSubjectClassification(2010):39-XX,41-XX,46-XX
© SpringerScience+BusinessMedia,LLC2014
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Preface
Handbook of Functional Equations: Functional Inequalities consists of 20 chap-
ters written by eminent scientists from the international mathematical community
who present important research works in the field of mathematical analysis and
related subjects with emphasis to functional equations and functional inequalities.
AsRichardBellmanhassoelegantlystatedatthesecondinternationalconference
ongeneralinequalities(Oberwolfach1978),“Therearethreereasonsforthestudy
of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he
said, “As has been pointed out, beauty is in the eye of the beholder. However, it
is generally agreed that certain pieces of music, art, or mathematics are beautiful.
Thereisanelegancetoinequalitiesthatmakesthemveryattractive.”Thechapters
of this book focus mainly on both old and recent developments on approximate
homomorphisms,onarelationbetweentheHardy–HilbertandtheGabrielinequal-
ity,generalizedHardy–HilberttypeinequalitiesonmultipleweightedOrliczspaces,
half-discreteHilbert-typeinequalities,affinemappings,contractiveoperators,mul-
tiplicativeOstrowskiandtrapezoidinequalities,Ostrowskitypeinequalitiesforthe
Riemann–Stieltjesintegral,meansandrelatedfunctionalinequalities,weightedGini
means, controlledadditiverelations, Szaz–Mirakyanoperators, extremalproblems
inpolynomialsandentirefunctions,applicationsoffunctionalequationstoDirichlet
problemfordoublyconnecteddomains,nonlinearellipticproblemsdependingonpa-
rameters,stronglyconvexfunctions,aswellasapplicationstosomenewalgorithms
forsolvinggeneralequilibriumproblems, inequalitiesfortheFisher’sinformation
measures, financial networks, mathematical models of mechanical fields in media
withinclusionsandholes.
Itisourpleasuretoexpressourthankstoallthecontributorsofchaptersinthis
book. I would like to thank Dr. Michael Batsyn and Dr. Dimitrios Dragatogiannis
fortheirinvaluablehelpduringthepreparationofthispublication.Lastbutnotleast,
I would like to acknowledge the superb assistance that the staff of Springer has
providedforthepublicationofthiswork.
Athens,Greece ThemistoclesM.Rassias
v
Contents
OnaRelationBetweentheHardy–HilbertandGabrielInequalities..... 1
VandanjavAdiyasurenandTserendorjBatbold
MathematicalModelsofMechanicalFieldsinMediawithInclusions
andHoles ........................................................ 15
MartaBryla,AndreiV.Krupoderov,AlexeyA.Kushunin,
VladimirMityushevandMichailA.Zhuravkov
ANoteontheFunctionsthatAreApproximatelyp-WrightAffine....... 43
JanuszBrzde¸k
MultiplicativeOstrowskiandTrapezoidInequalities .................. 57
PietroCerone,SeverS.DragomirandEderKikianty
A Survey on Ostrowski Type Inequalities for
Riemann–StieltjesIntegral ......................................... 75
W.S.CheungandSeverS.Dragomir
InvarianceintheFamilyofWeightedGiniMeans ..................... 105
IuliaCostinandGheorgheToader
Functional Inequalities and Analysis of Contagion
intheFinancialNetworks .......................................... 129
P.Daniele,S.Giuffè,M.Lorino,A.MaugeriandC.Mirabella
ComparisonsofMeansandRelatedFunctionalInequalities............ 147
WłodzimierzFechner
ConstructionsandExtensionsofFreeandControlledAdditiveRelations 161
TamásGlavositsandÁrpádSzáz
vii
viii Contents
ExtremalProblemsinPolynomialsandEntireFunctions .............. 209
N.K.GovilandQ.M.Tariq
OnApproximationPropertiesofSzász–MirakyanOperators........... 247
VijayGupta
Generalized Hardy–HilbertType Inequalities on MultipleWeighted
OrliczSpaces ..................................................... 273
JichangKuang
InequalitiesfortheFisher’sInformationMeasures.................... 281
ChristosP.KitsosandThomasL.Toulias
ApplicationsofFunctionalEquationstoDirichletProblemforDoubly
ConnectedDomains ............................................... 315
VladimirMityushev
Sign-Changing Solutions for Nonlinear Elliptic Problems
DependingonParameters .......................................... 327
D.MotreanuandV.V.Motreanu
OnStronglyConvexFunctionsandRelatedClassesofFunctions ....... 365
KazimierzNikodem
SomeNewAlgorithmsforSolvingGeneralEquilibriumProblems ...... 407
MuhammadA.NoorandThemistoclesM.Rassias
ContractiveOperatorsinRelationalMetricSpaces.................... 419
MihaiTurinici
Half-DiscreteHilbert-TypeInequalities,OperatorsandCompositions... 459
Bicheng Yang
SomeResultsConcerningHardyandHardyTypeInequalities.......... 535
NikolaosB.Zographopoulos
Contributors
VandanjavAdiyasuren Departmentof MathematicalAnalysis, NationalUniver-
sityof Mongolia,Ulaanbaatar,Mongolia
TserendorjBatbold Instituteof Mathematics,NationalUniversityof Mongolia,
Ulaanbaatar,Mongolia
Marta Bryla Department of Computer Sciences and Computer Methods,
PedagogicalUniversity,Krakow,Poland
Janusz Brzde¸k Department of Mathematics, Pedagogical University, Kraków,
Poland
Pietro Cerone Department of Mathematics and Statistics, La Trobe University,
Bundoora,Australia
W. S. Cheung Department of Mathematics, The University of Hong Kong,
Pokfulam,HongKong
IuliaCostin TechnicalUniversityCluj-Napoca,Cluj-Napoca,Romania
P. Daniele Department of Mathematics and Computer Science, University of
Catania,Catania,Italy
Sever S. Dragomir Mathematics, School of Engineering & Science, Victoria
University,MelbourneCity,MC,Australia
Włodzimierz Fechner Institute of Mathematics, University of Silesia, Katowice,
Poland
S. Giuffè D.I.M.E.T. Faculty of Engineering, University of Reggio Calabria,
ReggioCalabria,Italy
Tamás Glavosits Institute of Mathematics, University of Debrecen, Debrecen,
Hungary
N.K.Govil DepartmentofMathematicsandStatistics,AuburnUniversity,Auburn,
AL,USA
ix
x Contributors
VijayGupta DepartmentofMathematics, NetajiSubhasInstituteofTechnology,
NewDelhi,India
Eder Kikianty Department of Pure and Applied Mathematics, University of
Johannesburg,AucklandPark,SouthAfrica
ChristosP.Kitsos TechnologicalEducationalInstituteofAthens,Egaleo,Athens,
Greece
AndreiV.Krupoderov DepartmentofTheoreticalandAppliedMechanics,Belaru-
sianStateUniversity,Minsk,Belarus
JichangKuang DepartmentofMathematics,HunanNormalUniversity,Changsha,
P.R.China
AlexeyA.Kushunin DepartmentofTheoreticalandAppliedMechanics,Belarusian
StateUniversity,Minsk,Belarus
M. Lorino Department of Mathematics and Computer Science, University of
Catania,Catania,Italy
A. Maugeri Department of Mathematics and Computer Science, University of
Catania,Catania,Italy
C. Mirabella Department of Mathematics and Computer Science, University of
Catania,Catania,Italy
Vladimir Mityushev Department of Computer Sciences and Computer Methods,
PedagogicalUniversity,Krakow,Poland
D.Motreanu DépartementdeMathématiques,UniversitédePerpignan,Perpignan,
France
V.V.Motreanu DepartmentofMathematics,BenGurionUniversityoftheNegev,
Be’erSheva,Israel
KazimierzNikodem DepartmentofMathematicsandComputerScience,Univer-
sityofBielsko-Biala,Bielsko-Biala,Poland
MuhammadA.Noor COMSATSInstituteofInformationandTechnology,Islam-
abad,Pakistan
ThemistoclesM.Rassias DepartmentofMathematics,NationalTechnicalUniver-
sityofAthens,Athens,Greece
ÁrpádSzáz InstituteofMathematics,UniversityofDebrecen,Debrecen,Hungary
Q. M. Tariq Department of Mathematics and Computer Science, Virginia State
University,Petersburg,VA,USA
GheorgheToader TechnicalUniversityCluj-Napoca,Cluj-Napoca,Romania
ThomasL.Toulias TechnologicalEducationalInstituteofAthens,Egaleo,Athens,
Greece
Contributors xi
MihaiTurinici “A.Myller”MathematicalSeminar, “A.I.Cuza”University, Ias¸i,
Romania
BichengYang Department of Mathematics, Guangdong University of Education,
Guangzhou,Guangdong,P.R.China
MichailA.Zhuravkov DepartmentofTheoreticalandAppliedMechanics,Belaru-
sianStateUniversity,Minsk,Belarus
Nikolaos B. Zographopoulos Department of Mathematics & Engineering Sci-
ences,HellenicArmyAcademy,Athens,Greece