Table Of ContentSpringer Optimization and Its Applications 131
Nicholas J. Daras
Themistocles M. Rassias Editors
Modern
Discrete
Mathematics
and Analysis
With Applications in Cryptography,
Information Systems and Modeling
Springer Optimization and Its Applications
Volume 131
ManagingEditor
PanosM.Pardalos,UniversityofFlorida
Editor–CombinatorialOptimization
Ding-ZhuDu,UniversityofTexasatDallas
AdvisoryBoards
J.Birge,UniversityofChicago
S.Butenko,TexasA&MUniversity
F.Giannessi,UniversityofPisa
S.Rebennack,KarlsruheInstituteofTechnology
T.Terlaky,LehighUniversity
Y.Ye,StanfordUniversity
AimsandScope
Optimizationhasbeenexpandinginalldirectionsatanastonishingrateduringthe
lastfewdecades.Newalgorithmicandtheoreticaltechniqueshavebeendeveloped,
thediffusionintootherdisciplineshasproceededatarapidpace,andourknowledge
ofallaspectsofthefieldhasgrownevenmoreprofound.Atthesametime,oneof
themoststrikingtrendsinoptimizationistheconstantlyincreasingemphasisonthe
interdisciplinarynatureofthefield.Optimizationhasbeenabasictoolinallareasof
appliedmathematics,engineering,medicine,economicsandothersciences.
The series Springer Optimization and Its Applications publishes undergraduate
and graduate textbooks, monographs and state-of-the-art expository works that
focusonalgorithmsforsolvingoptimizationproblemsandalsostudyapplications
involvingsuchproblems.Someofthetopicscoveredincludenonlinearoptimization
(convex and nonconvex), network flow problems, stochastic optimization, optimal
control, discrete optimization, multi-objective programming, description of soft-
warepackages,approximationtechniquesandheuristicapproaches.
Moreinformationaboutthisseriesathttp://www.springer.com/series/7393
Nicholas J. Daras • Themistocles M. Rassias
Editors
Modern Discrete
Mathematics and Analysis
With Applications in Cryptography,
Information Systems and Modeling
123
Editors
NicholasJ.Daras ThemistoclesM.Rassias
DepartmentofMathematics DepartmentofMathematics
HellenicMilitaryAcademy NationalTechnicalUniversityofAthens
Vari,Greece Athens,Greece
ISSN1931-6828 ISSN1931-6836 (electronic)
SpringerOptimizationandItsApplications
ISBN978-3-319-74324-0 ISBN978-3-319-74325-7 (eBook)
https://doi.org/10.1007/978-3-319-74325-7
LibraryofCongressControlNumber:2018943447
MathematicsSubjectCodes(2010):06-XX,11T71,11YXX,14H52,14G50,34L25,34A34,41A05,
41-XX,49M30,60G25,65C20,68M10,68M12,68P25,68P30,68U20,74J20,78A46,81U40,81P94,
90B10,90B20,90C90,94A05,94A15,94A60,97R30,97R60,97U70
©SpringerInternationalPublishingAG,partofSpringerNature2018
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Preface
Modern Discrete Mathematics and Analysis with Applications in Cryptography
consists of contributions written by research scientists from the international
mathematicalcommunity.
The chapters are devoted to significant advances in a number of theories and
problemsofmathematicalanalysisbothcontinuousanddiscretewithapplications.
These chapters focus on both old and modern developments of mathematics.
Thevolumealsopresentsafewsurveypaperswhichdiscusstheprogressmadein
broader areas which could be particularly useful to graduate students and young
researchers.
We would like to express our deepest thanks to the contributors of chapters as
well as to the staff of Springer for their excellent collaboration in the presentation
ofthispublication.
Vari,Greece NicholasJ.Daras
Athens,Greece ThemistoclesM.Rassias
October2017
v
Contents
FixedPointTheoremsinGeneralizedb-MetricSpaces...................... 1
HassenAydiandStefanCzerwik
Orlicz Dual Brunn-Minkowski Theory: Addition, Dual
QuermassintegralsandInequalities ........................................... 11
Chang-JianZhaoandWingSumCheung
ModelingCyber-Security........................................................ 39
NicholasJ.DarasandArgyriosAlexopoulos
SolutionsofHardKnapsackProblemsUsingExtremePruning............ 81
E.Daravigkas,K.A.Draziotis,andA.Papadopoulou
AComputationalIntelligenceSystemIdentifyingCyber-Attacks
onSmartEnergyGrids.......................................................... 97
KonstantinosDemertzisandLazarosIliadis
RecentDevelopmentsofDiscreteInequalitiesforConvexFunctions
DefinedonLinearSpaceswithApplications.................................. 117
SilvestruSeverDragomir
ExtrapolationMethodsforEstimatingtheTraceoftheMatrixInverse... 173
ParaskeviFika
MomentGeneratingFunctionsandMomentsofLinearPositive
Operators ......................................................................... 187
VijayGupta,NehaMalik,andThemistoclesM.Rassias
ApproximationbyLupas.–KantorovichOperators........................... 217
VijayGupta,ThemistoclesM.Rassias,andDeepikaAgrawal
Enumerationbye ................................................................ 227
MehdiHassani
vii
viii Contents
Fixed Point and Nearly m-Dimensional Euler–Lagrange-Type
AdditiveMappings............................................................... 235
HassanAzadiKenary
DiscreteMathematicsforStatisticalandProbabilityProblems ............ 251
ChristosP.KitsosandThomasL.Toulias
OntheUseoftheFractalBox-CountingDimension
inUrbanPlanning ............................................................... 275
KonstantinaLantitsou,ApostolosSyropoulos,andBasilK.Papadopoulos
Additive-Quadraticρ-FunctionalEquationsinBanachSpaces ............ 281
JungRyeLee,ChoonkilPark,andThemistoclesM.Rassias
DeBruijnSequencesandSuffixArrays:AnalysisandConstructions..... 297
KonstantinosLimniotis,NicholasKolokotronis,andDimitriosKotanidis
FuzzyEmpiristicImplication,ANewApproach............................. 317
KonstantinosMattasandBasilK.Papadopoulos
AdaptiveTrafficModellingforNetworkAnomalyDetection............... 333
VassiliosC.Moussas
BoundsInvolvingOperators-Godunova-Levin-DragomirFunctions ..... 353
Muhammad Aslam Noor, Muhammad Uzair Awan,
andKhalidaInayatNoor
Closed-Form Solutions for Some Classes of Loaded Difference
EquationswithInitialandNonlocalMultipointConditions ................ 363
I.N.ParasidisandE.Providas
Cauchy’sFunctionalEquation,Schur’sLemma,One-dimensional
SpecialRelativity,andMöbius’sFunctionalEquation....................... 389
TeerapongSuksumran
Plane-Geometric Investigation of a Proof of the Pohlke’s
FundamentalTheoremofAxonometry........................................ 397
ThomasL.Toulias
DiagonalFixedPointsofGeometricContractions ........................... 423
MihaiTurinici
AMoreAccurateHardy–Hilbert-TypeInequality
withInternalVariables.......................................................... 485
BichengYang
AnOptimizedUnconditionallyStableApproachfortheSolutionof
DiscretizedMaxwell’sEquations............................................... 505
TheodorosT.Zygiridis
Contributors
Deepika Agrawal Department of Mathematics, Netaji Subhas Institute of Tech-
nology,NewDelhi,India
ArgyriosAlexopoulos CroisySurSeine,France
MuhammadUzairAwan GCUniversity,Faisalabad,Pakistan
Hassen Aydi Department of Mathematics, College of Education in Jubail, Imam
AbdulrahmanBinFaisalUniversity,Jubail,SaudiArabia
Wing Sum Cheung Department of Mathematics, The University of Hong Kong,
Pokfulam,HongKong
Stefan Czerwik Institute of Mathematics, Silesian University of Technology,
Gliwice,Poland
Nicholas J. Daras Department of Mathematics, Hellenic Military Academy, Vari
Attikis,Greece
E. Daravigkas Department of Informatics, Aristotle University of Thessaloniki,
Thessaloniki,Greece
Konstantinos Demertzis School of Engineering, Department of Civil Engineer-
ing, Faculty of Mathematics Programming and General Courses, Democritus
UniversityofThrace,Xanthi,Greece
Silvestru Sever Dragomir Mathematics, College of Engineering & Science,
VictoriaUniversity,MelbourneCity,MC,Australia
DST-NRFCentreofExcellenceintheMathematicalandStatisticalSciences,School
of Computer Science & Applied Mathematics, University of the Witwatersrand,
Johannesburg,SouthAfrica
K. A. Draziotis Department of Informatics, Aristotle University of Thessaloniki,
Thessaloniki,Greece
ix
x Contributors
Paraskevi Fika National and Kapodistrian University of Athens, Department of
Mathematics,Athens,Greece
VijayGupta DepartmentofMathematics,NetajiSubhasInstituteofTechnology,
NewDelhi,India
MehdiHassani DepartmentofMathematics,UniversityofZanjan,Zanjan,Iran
LazarosIliadis SchoolofEngineering,DepartmentofCivilEngineering,Faculty
of Mathematics Programming and General Courses, Democritus University of
Thrace,Xanthi,Greece
Hassan Azadi Kenary Department of Mathematics, College of Sciences, Yasouj
University,Yasouj,Iran
ChristosP.Kitsos TechnologicalEducationalInstituteofAthens,Athens,Greece
NicholasKolokotronis DepartmentofInformaticsandTelecommunications,Uni-
versityofPeloponnese,Tripoli,Greece
Dimitrios Kotanidis School of Pure and Applied Sciences, Open University of
Cyprus,Latsia,Cyprus
KonstantinaLantitsou DemocritusUniversityofThrace,Xanthi,Greece
JungRyeLee DepartmentofMathematics,DaejinUniversity,Pocheon,Republic
ofKorea
Konstantinos Limniotis School of Pure and Applied Sciences, Open University
ofCyprus,Latsia,Cyprus
HellenicDataProtectionAuthority,Athens,Greece
Neha Malik Department of Mathematics, Netaji Subhas Institute of Technology,
NewDelhi,India
Konstantinos Mattas Democritus University of Thrace, Department of Civil
Engineering,Xanthi,Greece
Vassilios C. Moussas Laboratory of Applied Informatics, Department of Civil
Engineering,UniversityofWestAttica,Egaleo-Athens,Greece
KhalidaInayatNoor COMSATSInstituteofInformationTechnology,Islamabad,
Pakistan
Muhammad Aslam Noor Mathematics Department, King Saud University,
Riyadh,SaudiArabia
COMSATSInstituteofInformationTechnology,Islamabad,Pakistan
Basil K. Papadopoulos Democritus University of Thrace, Department of Civil
Engineering,Xanthi,Greece
Contributors xi
A. Papadopoulou Department of Mathematics, Aristotle University of Thessa-
loniki,Thessaloniki,Greece
I. N. Parasidis Department of Electrical Engineering, TEI of Thessaly, Larissa,
Greece
Choonkil Park Research Institute for Natural Sciences, Hanyang University,
Seoul,RepublicofKorea
E. Providas Department of Mechanical Engineering, TEI of Thessaly, Larissa,
Greece
ThemistoclesM.Rassias DepartmentofMathematics,NationalTechnicalUniver-
sityofAthens,Athens,Greece
Teerapong Suksumran Center of Excellence in Mathematics and Applied,
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang
Mai,Thailand
ApostolosSyropoulos GreekMolecularComputingGroup,Xanthi,Greece
ThomasL.Toulias TechnologicalEducationalInstituteofAthens,Egaleo,Athens,
Greece
Mihai Turinici A. Myller Mathematical Seminar, A. I. Cuza University, Ias¸i,
Romania
Bicheng Yang DepartmentofMathematics,Guangdong UniversityofEducation,
Guangzhou,Guangdong,People’sRepublicofChina
Chang-Jian Zhao Department of Mathematics, China Jiliang University,
Hangzhou,People’sRepublicofChina
Theodoros T. Zygiridis Department of Informatics and Telecommunications
Engineering,UniversityofWesternMacedonia,Kozani,Greece
