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2SHANKARAPAILOORconcludesection2.1bydeningthesenotions.Webeginsection

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4SHANKARAPAILOORCorollary2.7.LetMbecompactandf:M!N...

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H// YIev0 Xf// Ywheref:X!Yisanarbitrarymap.Thesp...

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2GRAPHICALANALYSIS,ANDATTRACTINGANDREPELLINGFIXEDPOINTS62GraphicalAnal

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2];n=7,xi=i 2n.DerivativeApproximations:iff(x)2C...

(z)#!.Clearly,F(f)isopenandJ(f)isclosed,whileingeneral,I(f)isneitherop

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"#"e andf(#( andhence .If ,1},thendifferentiationy...

thenf(x)isnotone-to-one.Thereasonf(x)wouldnotbeone-to-oneisthatthegrap

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amoremathematicallanguage:fisone-to-one graphoff(x...

Theorem1Iff(n)andg(n)aretwonegligiblefunctions,thentheirsumh(n)=f(n)+g

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Corollary2Iff(n)isnon-negligibleandg(n)isnegligibl...

1.Letf(x)=x3;thenf1(x)=3p

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x;sincef1(f(x))=3p x3=xandf(f1(x))=(3p x)3=x: 3....

94Theorem22.3.SupposecharF=0.Iff(x)2F[x]issolvablebyradicalsthenGfisas

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E(w)=Mr=M (e)=Hr Fr1 Fr1(w)=Mr1 G(Mr=Mr1...

68L.C.Ciungufuzzystructuresconstructedfromcontinuoust-normsandtheywere

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70L.C.Ciungu(2)IfX=xwewrite[x)insteadof[fxg)and[x)...

oflabels,intermsoftheactionsthatarepermittedorde-nied.Thisobservationi

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simple(acl:lab,x:intfaclg)=if(memberuseracl)thenf...

$Internat.J.Math.&Math.Sci.VOL.21NO.4(1998)643-652643HOMOGENEOUSCONESAN$

Internat.J.Math.&Math.Sci.VOL.21NO.4(1998)643-652643HOMOGENEOUSCONESAN

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306OKadaWTakahashiretractionontothesetofcommon12xedpointsRecentlyTakah

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