38圆园191212允韵哉砸晕粤蕴韵云宰哉再陨哉晕陨灾耘砸杂陨栽再武夷学院学报灾燥造援38晕燥援12Dec援圆园19Schurer型Durrmeyer算子在Orlicz空间内的逼近渊袁354300冤DurrmeyerOrlicz摘要院袁Hardy,JensenSchurer遥Durrmeyer曰Orlicz曰曰关键词院Schurer中图分类号:O174.41文献标志码:A文章编号院员远苑源原圆员园怨穴圆园19雪12原园001原园3Orliczf渊x冤院棕1,M渊f,t冤=sup椰f渊x+h冤-f渊x冤椰M袁u0>0袁k>0袁u逸u0袁M渊2u冤臆kM渊u冤袁NM渊u冤驻2[9]遥Ramazanov渊1984冤[10]袁棕1,M渊f,t冤寅0渊t寅0冤,棕2,M渊f,t冤寅0渊t寅0冤遥c遥Orlicz定理1f袁nLM*袁Orlicz[1原7]袁遥Cabulea渊2002冤[8]SchurerDurrmeyer院Dn渊f曰x冤=渊n+p+1冤移pn+p,k渊x冤k=0n+pf沂C咱0,1+p暂袁x沂咱0,1暂,n沂N,p沂N胰喳0札,n+pkn+p-kpn+p,k渊x冤=x渊1-x冤遥kC觍bulea[8]Dn渊f曰.冤[0,1]*蓸蔀乙10pn+p,k渊t冤f渊t冤dt,渊1冤棕2,M渊f,t冤=sup椰f渊x+h冤+f渊x-h冤-2f渊x冤椰M遥0臆h臆t0臆h臆t遥袁M渊u冤遥OrliczN渊淄冤N[9]遥NOrliczNM渊u冤驻2袁LM*遥,NM渊u冤Orlicz袁LM*遥*Orlicz籽渊淄袁N冤臆1LM椰u椰M=sup喳u渊x冤札袁N渊淄冤遥籽渊淄袁N冤=10乙10LM*椰Dn椰M臆1遥定理2Dn渊f曰.冤袁u渊x冤淄渊x冤dxM渊窑冤驻2袁乙10N渊淄渊x冤冤dx淄渊x冤n+p逸3袁椰Dn渊f曰.冤-f椰M臆c棕1,M渊f,定理3M渊窑冤姨n+p+211f沂LM,冤遥*[9]袁Orlicz驻2袁f沂LM,冤遥Orlicz椰u椰M=infa>011+a蓘乙院M渊au渊x冤冤dx遥蓡n+p逸3袁椰Dn渊f曰.冤-f椰M臆c棕2,M渊f,姨n+p+22几个引理引理1[8]渊1冤1冤Dn渊1;x冤=1曰2冤Dn渊t;x冤=Dn渊f曰.冤袁收稿日期院2019原07原18基金项目院作者简介院袁袁渊2018J01428冤遥袁(1965原)袁遥渊n+p冤x+1;n+p+2窑2窑叶曳圆园19123冤Dn渊t2;x冤=渊n+p冤渊n+p-1冤x2+4渊n+p冤x+2引理2渊1冤渊n+p+2冤渊n+p+D3冤.冤袁遥n1冤D渊f曰n渊渊t-x冤;x冤臆n+p+32;2冤n+p逸3袁Dn渊渊t-x冤2;x冤臆n+p+12遥1冤院x沂[0,1]袁1Dn渊渊2冤t-x冤;x冤臆n+p+32遥maxn+p1逸3袁1袁x沂[0袁1]x渊1-x冤=D4袁n渊渊t-x冤2;x冤=Dn渊t2;x冤-2xDn渊t;x冤+x22渊渊n+p-n+p+3冤2冤渊x渊1=n+p+-x冤+23冤臆n+p+12遥引理3[10]M渊窑冤驻2袁f沂L*M,兹*f渊x冤沂LM,椰兹f渊x冤椰M臆c椰f椰M袁兹f渊x冤=0臆sup1渊u冤duf渊x冤Hardyt屹t臆1xt-x遥乙txff渊x冤沂L*咱0,1暂袁f渊x冤=0遥M,f渊x冤[0,1]袁x埸g渊x冤=1t乙t*0f渊x+u冤du袁g渊x冤沂LM椰1椰gg-f椰M臆椰椰f椰M袁椰g'椰M臆t棕1,M渊f,t冤,M臆棕1,M渊f,t冤遥引理4g渊x冤沂L*-g椰M臆姨n+p+cM袁n+p逸3袁椰Dn渊g曰.冤2椰g'椰M遥院x冤-gx渊沂[0,1]袁x冤=1Dn渊g曰讦渊n+p+1冤移n+pk=0pn+p,k渊x乙冤渊t冤蓘渊n+p+1冤移n+p1乙10pn+p,kk=0pn+p,k渊x冤兹0pn+p,k渊t冤讦g'乙g渊t冤-g渊x冤蓡dt讦臆tx讦g'渊u冤讦du讦dt臆渊x冤Dn渊讦t-x讦;xCauchy-Schwarz冤遥2Dn渊g曰x冤-g渊x冤臆兹g'渊x冤Dn渊讦t-x讦;x冤臆兹g'渊x冤[Dn渊渊t-x冤2;x冤]12臆3袁姨n+p+12兹g'渊x冤遥椰Dn渊g曰.冤-g椰M臆姨n1+p+2椰兹g椰'M臆姨nc+p+2椰g'椰M遥引理5[11]f渊x冤沂L*M1冤f*t\"沂LM;袁2冤椰ft-f椰M臆13冤椰f2棕2,M渊f,t冤曰t'椰M臆1t4冤椰ft\"椰M臆1棕2,M渊f,t冤曰t2棕2,M渊f,t冤曰tft渊x冤=2t2冤f渊x冤Steklov21t2乙-t2乙-t2蓘f渊x+u+淄冤+f渊x-u-淄蓡dud淄遥2定理的证明定理1N尧移n+pk=0pn+p,k渊x冤=1袁n+p,k渊t冤dt=n+p+11,Jensen椰Dn渊f曰.冤椰M=inf1a>01a咱1+0M渊aDn渊f曰x冤冤dx暂臆乙infa>01a咱1+1乙1移n+p乙乙10p0k=0pn+p,k渊x冤dxM渊渊n+p+1冤0pn+p,k渊t冤af渊t冤dx冤暂臆infa>01a咱1+乙1移n+p10k=0pn+p,k渊x冤dx乙0pn+p,k渊t冤M渊af渊t冤冤dtt暂=inf1咱1+移n+pppn+p,kn+p,k渊乙10渊t乙10pn+p,k渊t冤d冤M渊af渊t冤冤dta>0ak=0x冤dx暂=inf1移n+pa>01a咱1+0k=0p乙10pn+p,k渊t冤dtn+p,k渊t冤M渊af渊t冤冤dt暂=椰f椰M遥袁乙Dn渊f曰.冤袁Dn渊f曰.冤L*ML*M袁椰Dn椰M臆1遥*院SchurerDurrmeyer*Orlicz窑3窑定理2n+p逸3袁f渊x冤沂LM4g渊x冤沂LM袁棕2,M渊f,t冤+椰Dn渊f曰.冤-f椰M臆椰Dn渊f-g曰.冤-渊f-g冤椰M+椰Dn渊g曰.冤-g椰M臆渊1+椰Dn椰M冤椰f-g椰M+2棕1,M渊f,t冤+t=1c姨n+p+2c椰g'椰M臆c11渊棕2,M渊f,t冤+2棕2,M渊f,t冤冤遥tn+p+2t11t=,椰Dn渊f曰.冤-f椰M臆棕2,M渊f,冤遥n+p+2n+p+2姨姨参考文献院1棕1,M渊f,t冤遥t姨n+p+2椰Dn渊f曰.冤-f椰M臆c棕1,M渊f,f\"渊x冤沂LM袁2*[1]AKG俟NR,ISRAFILOVDM.Simultaneousandconverseap鄄MathSocSimonStevin,2010,17(1):13-28.proximationtheoremsinweightedOrliczspaces[J].BullBelg姨n+p+2渊1冤姨n+p+2袁1冤遥[2]CUENYAH,LEVISF,MARANOM,etal.Bestlocalapprox鄄2011,32(11):1127-1145.Jackson,.Orlicz[J]...定理3n+pn+p逸3imationinOrliczspaces[J].NumerFunctAnalOptim,KantorovichShepard((姿越员)[3]讦渊n+p+1冤移pn+p,k渊x冤k=0Dn渊f曰x冤-f渊x冤=3渊f'渊x冤+兹f\"渊x冤冤遥n+p+2袁咱9暂3椰Dn渊f曰.冤-f椰M=sup讦籽渊淄袁N冤臆1Dn渊渊t-x冤;x冤f'渊x冤+Dn渊渊t-x冤;x冤2乙),2014,43(6):674-679.10pn+p,k渊t冤渊t-x冤f'渊孜冤dt讦臆兹f\"渊x冤臆[4]Durrmeyer原Bernstein[J].(Orlicz),2016,25(6):550-553.[5]Orlicz,[J].Szasz-Kantorovich-Bezier,2017,33籽渊淄袁N冤臆13渊sup椰f'椰M渊1+籽渊淄袁N冤冤+n+p+2籽渊淄袁N冤臆1sup椰兹f\"椰M渊1+籽渊淄袁N冤冤冤臆c渊椰f'椰M+椰兹f\"椰M冤臆n+p+2c渊椰f'椰M+椰f\"椰M冤遥n+p+2乙10渊Dn渊f曰x冤-f渊x冤冤淄渊x冤dx讦臆[6]COSTARELLID,SAMBUCINIAR.Approximationresultsinneuralnetworkoperators[J].ResultsMath,2018,73(1):1-15.,[J]..Durrmeyer袁2019,39(6):1-4.Orlicz(2):168-176.OrliczspacesforsequencesofKantorovichmax-product[7][8][9]type[J].ActaUnivApulensisMathInform,2002,4(4):37-44.,,1983..[M].院CABULEALA,TODEAM.GeneralizationsofDurrmeyerft\"沂LM袁渊1冤椰Dn渊f曰.冤-f椰M臆渊2冤*f渊x冤沂LM袁*n+p逸3袁5[10]andrationalfunctionsinOrliczspaces[J].AnalMath,1984(10):117-132..Bernstein-DurrmeyerOrliczRAMAZANOVARK.Onapproximationbypolynomials[11]椰Dn渊f-ft曰.冤椰M+椰Dn渊ft曰.冤-ft椰M+椰ft-f椰M臆渊1+椰Dn椰M冤椰ft-f椰M+[J].袁1997,26(4):6-9.c渊椰ft'椰M+椰ft\"椰M冤臆n+p+2渊责任编辑院叶丽娜冤OnApproximationbySchurerTypeDurrmeyerOperatorsinOrliczSpaces(SchoolofMathematicsandComputerScience,WuyiUniversity,Wuyishan袁Fujian354300)RENMeiyingAbstract院Keywords院SchurertypeDurrmeyeroperators;Orliczspaces;modulusofcontinuity;degreeofapproximationInthispaper,approximationpropertiesofSchurertypeDurrmeyeroperatorsarestudiedinOrliczspacesbythetoolsofHardymaximalfunction,Jenseninequalityandmodulusofcontinuityandsoon.Andthedegreeofapproximationisobtained.
