简介：OnCopositiveInthispapertheauthorwritesasimplecharacterizationforthebestcopositiveapproximationtoelementsofC（Q）byelementsoffinitedimensionalstrictChebyshevsubspacesofC（Q）inthecasewhenQisanycompactsubsetofrealnumbers.AttheendofthepapertheauthorappliesthisresultfordifferentclassesofQ.

简介：InthissurveythenotionofabalancedbestmultipointlocalapproximationisfullyexposedsincetheyweretreatedintheLpspacesandrecentresultsinOrliczspaces.Thenotionofbalancedpoint,introducedbyChuietal.in1984areextensivelyused.

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简介：Inthispaper,wegivesomeresultonthesimultaneousproximinalsubsetandsimultaneousChebyshevintheuniformlyconvexBanachspaceAlsowegiverelationbetweenfixedpointtheoryandsimultaneousproximity.

简介：Thef(x)∈C[-1,1]isgiven,amodificationisgiventotheinterpolationpolynomialQn(f;x)(thepower,lessthanλn,1

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简介：Weadoptthefollowingsymbolsandnotations.LetC[0,1]Nbetheclassofallrealcontinuousfunctionsin[0,1]whichhaveNcontinuousderivatives,L[0,1]pbethespaceofrealpthpowerintegrablefunctionson[0,1],andΔk,asusual,betheclassofkthmonotonefunctions.

简介：Wegiveaconstructionofthemaximum,andtheminimumofthesetofnondecreasmgapproxmantsinthediscretecase,whereisapositiveconoexfunction.Acharacterizationofthatsetisalsoobtained.

简介：Let(Ω,A,P)beaprobabilityspace,X(t,ω)arandomfunctioncontinuousinprobabilityfort∈[0,∞)or(-∞,+∞)(ω∈Ω),andF(t)apositivefunctioncontinuousfort∈[0,+∞)or(-∞,+∞).IfX(t,ω)andF(t)verifycertainconditions,thenthereexistaasequence{Qn(t,ω)}ofrandompolynomialssuchthatwehavealmostsurely:fort[0,+∞)or(-∞,+∞),lim↑n→+∞|X(t,ω)-Qn(t,ω)|/F(t)=0.

简介：Inthispaper,wegivesomepropertiesoff-approximation,f-Chebyshevcentersandf-farthestpointsinlocallyconvexspaces.

简介：Westudythefleetsizeandmixvehicleroutingproblemwithconstraintsonthecapacityofeachvehicle.Theobjectiveistominimizethetotalcostincludingfixedutilizationcostofvehiclesandtravelingcostbyvehicles.Wegivedifferentialapproximationalgorithmsforthefleetsizeandmixvehicleroutingproblem(FSMVRP)withtwokindsofvehicles,thecapacitiesofwhicharerespectivelyn1kandn2k,n2>n1≥1,k≥1.Usingexistingtheoriesforvehicleroutingproblemsandfeatureofthealgorithmsrepresentedinthepaper,wealsoprovethatthealgorithmsgive(1-(6n+3/((n+1)2k+n+1))differentialapproximationratiofor(k,nk)VRP,n>1and(1-(6n2+3n1/(n1k+n2k)2k))differentialapproximationratiofor(n1k,n2k)VRP,n2>n1>1.

简介：Denotebyn（f）thedegreeofcopositiveapproximationtof（x）bypolynomialsofdegree≤n.Forfunctionf（x）∈Ck[-1,1]whichalternatesinsignfinitelymanytimesin[-1,1],theauthorobtainsthefollowingJacksontypeestimatesn（f）≤Cn-kw(fk,1/n)foaanypositiveintegerk.

简介：Weinvestigatetherelationshipbetweenbestapproximationsbyelementsofclosedconvexconesandtheestimationoffunctionalsonaninnerproductspace(X,<·,·>)intermsoftheinnerproductonX.

简介：Inthispaper,theapproximationforfourkindsofknapsackproblemswithmultipleconstraintsisstudied:0/1MultipleConstraintKnapsackProblem(0/1MCKP),IntegerMultipleConstraintKnapsackProblem(IntegerMCKP),0/1k-ConstraintKnapsackProblem(0/1k-CKP)andIntegerk-ConstraintKnapsackProblem(Integerk-CKP).Thefollowingresultsareobtained:1)UnlessNP=co-R,nopolynomialtimealgorithmapproximates0/1MCKPorIntegerMCKPwithinafactrok^(1/2)-σforanyσ>0;unlessNP=P,nopolynomialtimealgorithmapproximates0/1MCKPorInterMCKPwithinafactork^(1/4)^-σforanyσ>0wherekstandsforthenumberofconstraints.2)Foranyfixedpositiveintegerk,0/1k-CKPhasafullypolynomialtimeapproximationscheme(FPTAS).3)Foranyfixedpositiveintegerk,Integerk-CKPhasafastFPTASwhichhastimecomplexityO(n+1/ε^3+1/ε^3k+1-2)andspacecomplexityO(n+(1/ε^3)),andfindsanapproximatesolutiontowithinεoftheoptimalsolution.

简介：ＯＮＭ－ＩＤＥＡＬＳＡＮＤＢＥＳＴＡＰＰＲＯＸＩＭＡＴＩＯＮＨＡＮＤＥＧＵＡＮＧ（韩德广）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｑｕｆｕ２７３１６５，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａ...

简介：Weestablishtheconceptofshapesoffunctionsbyusingpartialdifferentialinequalites.Ourdefinitionaboutshapesincludessomeusualshapessuchasconvex,subharmonic,etc.,andgivesmanynewshapesoffunctions.Themainresultsshowthattheshapepreservingapproxi-mationhascloserelationtotheshapepreservingextension.Oneofourmainresultsshowsthatiff∈C（Ω）hassomeshapedefinedbyourdefinition,thenfcanbeuniformlyapproximatedbypolynomialsPn∈pn（n∈N）whichhavethesameshapeinΩ,andthedegreeoftheap-proximationisCω(f,n-β)withconstantsC,β>0.

简介：Theregularsolutionsofgeneralizedaxisymmetricpotentialequationarecalledgeneralizedaxisymmetricpotentials.Inthispaper,thecharacterizationsoflowerorderandlowertypeofentireGASPintermsoftheirapproximationerror{En}havebeenobtained.

简介：Inthispaper,weintroduceatypeofapproximationoperatorsofneuralnetworkswithsigmodalfunctionsoncompactintervals,andobtainthepointwiseanduniformestimatesoftheapproximation.Toimprovetheapproximationrate,wefurtherintroduceatypeofcombinationsofneuralnetworks.Moreover,weshowthatthederivativesoffunctionscanalsobesimultaneouslyapproximatedbythederivativesofthecombinations.Wealsoapplyourmethodtoconstructapproximationoperatorsofneuralnetworkswithsigmodalfunctionsoninfiniteintervals.

简介：让功能f∈C[1，1]，在有限收集Y:=改变它的monotonisity{y1，...，ys}s点yi∈(1，1)。为每n≥N(Y)，我们构造代数学的多项式Pn，度≤n，它是有f的comonotone，那是它在一样的monotonisity削尖的变化yi作为f，；