8 No8Vol JOURNALOF NEIJIANG NORMAL UNIVERSITY * * ( 6499) : ; ; ; ; ; : ; ; DOI:060/jcki-6/z0808006 :G647 :A :67-78(08)08-00-09 0 [4] [] [6] [7] ( ) ( [8] ) [9] [] : [] [] :08-06- : (ZG0464) (ZY600) 06 (T60009T6000T600) ( (0)) : (994-) : * : (96-) :
4 8 c +t +t - (t +t ) - <t +t < - < t t < + +c ( ) +t + ( ) +t + [ - (t +t )] (t + t ) + t + t t 0 + +c c x i R + (i ΔABC ABC ) x i x i c ABC 0 ABC AC DBD 4+c ABC 0 ABC AC DBD c>0 4 -+ +cc 4+c 4 -c0 + -4 + c S ΔABC csi0 si60 + csi60 +ccc - ( >) c - 4+c4+ - +4 (-)+ (-) + 4(-) 槡 (- ) +9 4(-) - c 4+c 9 8 ( -) ] 8 c + mx 8 c 槡 c 4 - +4 -c0c0-4 + c ( - ) - - Δx ( -4 + c ) - mi c R + ++c + 4 c +c i i c 8 ( +) + 8 ( -) + c0-4 + c 4 -+4 -c0c>0 c 8 ( +) + 8 ( -) (+) 8 [ c- 4 c R + ++c0< 4 f(x)x +x+c( c< c c ) f (x) x R f(x) f (x) +c
088 : x R f(x) f (x) st 4 si θ ( 0] f(s) 8 4c-4 s +s 4( c 4c-4 - ) f()9 s 4 + t +c +c ( c ) + 8 t 4 si θ +t4 si θ 4 +9 xy t f (x)x+ x Rf(x) f (x) x Rx + (- )x+c- 0 <0 { Δ -4c+4 0 4( c 4c-4 - ) +c +c ( c ) + c t <0 { 4(c-) 0 t t 0;t> +c +c 4(t-) t + 4 (t-)+ 槡 - t- + xy 0 x +y u 4 + +4x y x +y x y x +y t x tcosθy tsiθ 0<t 0<θ π c 4 + 8 t t 4 si θ +t4 si θ u mi (-) 6 >>u 槡 -+ 槡 -4 槡 -x 槡 -4 y 槡 - x 槡 -4 y 槡 x + 槡 y +4 (-) 槡 -+ 槡 -4 ( 槡 x ++ 槡 y +4) x +y + 槡 (x +)(y +4)+ t 槡 +c ( 槡 +) 4槡 x +y + 槡 x y +4x +y +4+ +c 槡 - x +y + 槡 x y +4xy +4+ x +y +xy +9 ( ) +9 6 ( ) xy 槡 槡 u mi 6 7 x +y t c R + c- 4c- si θ+cos θ cl +clc c
6 8 cxx- 4x- + 4 f(x) mi f( e ) - e - e 0 e 7 e 8 >>c>0 + + (-) - 0c+c ( ) A B4 C 槡 D c 4t -t+4 + (t+) 槡 (4t +4t+) ( 6t- 4t -t+4 + ) c 槡 8 c 槡 c f(c) + + (-) -0c+c f (c)-0+0c f (c)0 c c f(c) f(c) f( ) + + (-) g() + + (-) g ()- + g() g() g( ) + 4 h() + 4 h() h () x + + 4 + 7-8 ()0 槡 h xl +xlx x 0 R + x 0lx 0 - 槡 h() h ( 槡 )4 x 0l+ 0f(x)xlx-xl+ f(c) g() h() 4 B f (x) mi 0f (x)lx-l+f 0 x e 4 x (0 e ) f (x)<0f(x)(0 e ) ;x ( e 4 + #)f (x) > 0 f(x)( e + #) t c 4t -t+4 + 槡 (4t +4t+) + c0-4 + c t tt t 4 -+4 -c0c 0-4 + c ( - ) - - 4 c - 4 + c - 4 c f(c) 9 g (-) ()0 c + +c + c c k k k ck cf(
088 : 7 c) y 0c 0 k k x+ 槡 m 0 槡 y- 0m+ k ck c k 0k 0 f(c) c k c + kc k c+c +kc c k + k k + + (k +) - 槡 k k k + ( k +)- k (- t+ k k + k + k k 0 c 0 f (c) mi 0 xyz z U mi 7 xy +yz+zx x +y +z xy λ μ R + xyyzxz x y z (x (λx) (λy) λ +y ) xy x +y (λy) ( μ z) λ y +μ z yz λ μ y + μ λ z ( μ z) (λx) μ z +λ x zx μ λ z + λ μ x U xy +yz+zx (λ μ + ) x + ( λ μ + ) y + μ λ z ( λ μ + ) x + ( λ μ + ) y + μ λ z x +y +z (*) λx λy μz (*) λ μ + μ λ μ λ t (t>0) t t + t + 槡 8 μ λ + 槡 8 ( *) U + 槡 4 x y z4 4 ( 槡 -) U + 槡 4 4 x+ 槡 + 槡 y- zx+ -t 0 m +t- z m + + + (+t-) + -(t+)+ (t+) + ) + ( t+) + ( t+) + 7 t+ t 0x 4 y 4 槡 + ( 0 0) λ μ R + >0>0 : + 槡 + 槡 + 槡 槡 + 槡 4槡 槡 + 4槡 ( + ) ( + )( + ) xy 4x +y +xy 4x +y + xy ( ) 槡 +( x ) :x+ y + ( ) ( 槡 ) + ( 槡 槡 槡 槡 0 ( ) 槡 x 槡 0 x ) 槡 x y 槡 0 x xy+ y +
8 8 () x y 0<α< i i >0 (i ) α+ α + α+ α + + α+ α ( + + + ) α+ ( + + + ) ; α 4 xy x +y -x+4y+ α< 0 α > i i > 0 (i ) 0 y x + α+ α + α+ α + + α+ α ( + + + ) α+ ( + + + ) ; α [0] y x + k kx -y+k 0 x +y -x+4y+ 0 (kx -k) 4k + ( y-) 4 4k +4 (kx -y+-k) (-k) 0 k y x + [0 ] 4 xt R + N + x -i ti x -i - i (i -) x t -i t i-x t - x-(-)t [] xyz R + x + 槡 y+z S x +y + z x x - y 6y- 槡 槡 y- z c z- 0 c S x +y + z - ( + + 0 c ) xyz c 槡 c x 槡 y z 槡 x + 槡 y+z ( 槡 + ( 槡 ) + 槡 槡 槡 Smi 0 8 9 x z 槡 y 8 ) z x+ +y- + :z ( 槡 x++ 槡 y-) + + x+ 槡 + 槡 y- z 7 槡 x+ 槡 y- 槡 x++ 槡 y- x 4 y 4 z mi 7 4 ( : k y x + ykx+k ) 6 6 7 c c- 4c- c 4c- c cl +clc cl- cl +clc-cll c +lc c- 4c- c- -4c+c- 0c 4c
088 : 9-4 - 7 >0 7 cl +clc cl-cl +clc- clcl +clc c>0 l c + l c f(x) x +lx f (x) x- x xf(x) mi f() l e 7 e 6 xyz>0+z 槡 x +x + 槡 t C+t A 槡 6 6 槡 y +y + 槡 z +z 8 xyz (0) - + f(x) 槡 x +x ( -y+z + -z+x 0<x <) f(x) xyz>0+z f(x)x (0) M 槡 x f(x) +x ( 0<x <)f (x) -x 槡 x (+x) <0 f (x) x -6x- 4x (+x) <0 f(x)x (0) 槡 x +x + 槡 y +y + 槡 z +z f (x)+f(y)+f(z) f( +z ) 槡 4 x y z - - 槡 4 6 7 ΔABC t 槡 A+t B + 槡 t B+t C+ 槡 t C+t A ) - - ΔABC (x- x i ) + (y- yi) ( 槡 x +y z ta+itbz tb+ itcz tc+ita z +z +z (ta+tb+tc)(+i) z +z +z z + z + z 槡 t A +t B + 槡 t B+t C+ 槡 t C+t A 槡 (ta +tb+tc) ta +tb + tc 槡 槡 t A +t B + 槡 t B+t C+ 槡 t C+t A 槡 6 槡 t A +t B + 槡 t B+t C + - + -y+z + -z+x N (-)+ (-y+z)+ (-z+x)m+n - + (-)+ -y+z + (-y+z)+ -z+x + (- z+x) ++6N M - + -y+z + -z+x 64 (x y) (x y) (x -x ) + (y -y) ( 槡 x +y - x 槡 +y ) (xy) c i c i (x i yi)(i i i - i i 槡 x i +y i)
40 8 c i 9 f(xyz) (x-y-z) + ( 4 x - 槡 -y - 槡 -z ) (x 4 x ) c (y 槡 -y (z 槡 -z ) (x-y-z) + ( 4 x - )c 槡 -y - 槡 -z ) PF + PA PA - PF +8 AF +88+ 槡 PP ( 槡 x +y -4x+ 4+ 槡 x +y -x+4y+ ) mx 8+ 槡 槡 [ x + 6 - ( y 槡 + ( 槡 -y ) + 槡 z + ( 槡 -z x ( 槡 8- (+ 槡 ) ) - 槡 ) ] x y 4 槡 -y z x 4 槡 -z x x (xyz) ( 槡 ) f(xyz) mi - 槡 clc c + c c + c 4 c e c x c y c x y 7 : [] (xy) ( )P(x 0 y0)ye x ye x 0 x+ e x 0(-x 0 )ye x yex 0 xy x +4y 48 槡 x +y -4x+ 4 + 槡 x +y -x+4y+ P(xy)P Γ: x 6 +y P A(-) F (0) PF - PF PA - PF +8 P AF xoy P(xy) Γ: x 6 +y 8 Γ F (-0)F (0) A(-) AF Γ P 槡 x +y -4x+ 4+ 槡 x +y -x+4y+ 7 c- 4c-cl + 4y e x y x y x e koa y x ( y x ) 7 mx 7 e ΔABC f(abc) 9tAtB+tBtC+tAtC f(abc)f(bac)ab A B
088 : 4 f(abc) A B A B 9t A+ : tatc A +B+Cπ 9t A+tAtC9 t A+ 4tA t A- +49 (t A-)+ 4tA t A- + 008():4-44 6+ t A- [] [J] 06():-7 [] [J] [] [J] ( )06(8):64-67 t A [4] [J] 07():-4 [] [J] 0(4):80-8 [] [6] 00 () [J] 00(0):-7 [7] [J] 06():46-47 [8] [J] 006(4):9- [9] [J] 0 (4):6-6 [0] [J] 000(6):9-9 [] [J] 00():40-4 [] [J] 0(4):- StrtegiesforSolvigtheMximum VlueofMultivriteFuctios WANGXiyiZHAOSili (ColegeofMthemticsdIformtioScieceNeijigNormlUiversityNeijigSichu6499Chi) Astrct: Somestrtegiesforsolvigtheextremevlueprolemsreltedtomultivritefuctiosweresummedup i- cludigtheelimitiostrtegycommuttiostrtegypriciplelemetstrtegyvrilesitroductiostrtegycostruc- tiostrtegycomitiostrtegyofumerdformsymmetrystrtegyetcofwhichtheelimitiostrtegiesiclude sustitutiolelimitioicremetlelimitiomtchigelimitioreductioelimitiodsoforth;thesustitutio strtegyicludestrigoometricsustitutioitegrlsustitutiodsoothestrtegyreltedtotheitroductioofvri- lesicludestheitroductioofoeprmetertwoprmetersswelsmultipleprmetersiequlitystrtegycotis methodslikemeiequlitycuchyiequlityelipticiequlitypowerreductioiequlityweightigiequlitiesetc Costructiostrtegyicludescostructedfuctiocostructedcomplexumerscostructeddulitydcostructedvectors dsoothepplictioofthecomiedstrtegyofumersdshpestogetherwiththesymmetricstrtegiesisolvig theextremevlueprolemsreltedto multivritefuctiosisfoudtoequickdcocisethesestrtegiesd methods hveeeusedtolyzedsolvesometypiclprolems Keywords: multivritefuctio ;extremevlue;prolem-solvigstrtegy ( : )