A NEW GENERALIZATION OF NESBITT S INEQUALITY

Transcription

1 Jourl of Siee Ars Yer No ORIGINAL PAPER A NEW GENERALIZATION OF NESBITT S INEQUALITY DUMITRU M. BĂTINEŢU-GIURGIU NECULAI STANCIU Musri reeie: ; Aee er: ; Pulishe olie: Asr. This er reses reroseie of our refiees eesios geerlizios of Nesi s iequliy. Also we rese ew geerlizio for his rerle iequliy. Keywors: Ro s iequliy Bergsrö s iequliy Jese s iequliy Nesi s iequliy.. INTRODUCTION I his seio we will o reroseie of our resuls o Nesi s iequliy:.. ON NESBITT S INEQUALITY FOR TWO VARIABLES If R he: A see for e.g. [6 ]... If R { } > he: B see [6 ]... ON NESBITT S INEQUALITY FOR THREE VARIABLES If R he: C Nesi90 see [ ].... If R he: D see [ ]. Mei Bsr Niol College Buhres Roi. E-il: _g@yhoo.o. George Eil Ple Shool 065 Buzău Roi. E-il: siueuli@yhoo.o. ISSN: Mheis Seio

2 56 A ew geerlizio of Nesi s iequliy Duiru M. Bieu-Giurgiu Neuli Siu... If R he: E see [ ].... If R { } > he: F see [ ]...4. If R he: [ suh h { } > G see [ ]...5. If R R he: H see []...6. If y z R he: I y z y z y z y z z y y yz z y yz z see [ 4]. y yz z..7. If y z R R he: y z J y z see []. y z z y y z.. ON NESBITT S INEQUALITY FOR VARIABLES: If R he: N see for e.g [4] he se 4 lso []. Mheis Seio

3 A ew geerlizio of Nesi s iequliy Duiru M. Bieu-Giurgiu Neuli Siu If N { } [ > he: R K... If R y R { } N see []. > y 0 R he: L see []. y... If N { } R R > he: M see [5]...4. If R R > he: [ U see [7] lso [0]...5. If R R > he: [ V see [8]...6. If N { } R R [ r s suh h > he: W r r s r s rs rs see [9 ]. ISSN: Mheis Seio

4 A ew geerlizio of Nesi s iequliy Duiru M. Bieu-Giurgiu Neuli Siu Mheis Seio If { } N R R we eoes he: Y will er i h Jourl Rereţii Meie...8. If { } N R R R suh h > he Z will er i h Jourl Rereţii Meie.. MAIN RESULTS Theore. If { } N R R R [ suh h > he Proof. WLOG we ssue h:... he: - he sequee is eresig - he sequee is iresig - he sequee is eresig. By Cheyshe s iequliy for eresig sequees reseiely we oi h: U

5 A ew geerlizio of Nesi s iequliy Duiru M. Bieu-Giurgiu Neuli Siu ISSN: Mheis Seio 59 By J. Ro s iequliy we he h: Also y J. Ro s iequliy we eue h: 4 By 4 we oi h: U he roof is olee. Rers. If we e i he 5 i.e. we reoi..8. If we e i 5 0 he: 6 If we e i 6 he we oi: 7 where. Filly if i 7 we e he we oi: N i.e. Nesi s iequliy for riles.

6 60 A ew geerlizio of Nesi s iequliy Duiru M. Bieu-Giurgiu Neuli Siu REFERENCES [] Băieţu-Giurgiu D.M. Siu N. Ariole și Noe Meie [] Băieţu-Giurgiu D.M. Siu N. Ariole și Noe Meie [] Băieţu-Giurgiu D.M. Beze M. Siu N. Mheil Euio i he Curre Euroe Coe [4] Băieţu-Giurgiu D.M. Siu N. R.M.T [5] Băieţu-Giurgiu D.M. Siu N. Sliire Miţii [6] Băieţu-Giurgiu D.M. Siu N. Dii Meiă 0. [7] Băieţu-Giurgiu D.M. Siu N. Eerieţe Uile î Prere-Îăţre Meiii 6 0. [8] Băieţu-Giurgiu D.M. Siu N. The Aeri Mheil Mohly [9] Băieţu-Giurgiu D.M. Siu N. Reis Esolr e l Olii Ieroeri e Meiá [0] Băieţu-Giurgiu D.M. Siu N. The Tehig of Mheis 6 0. [] Băieţu-Giurgiu D.M. Siu N. Oogo Mheil Mgzie [] Băieţu-Giurgiu D.M. Siu N. Jourl of Siee Ars [] Nesi A.M. Prole 54 Euiol Ties [4] Zoru T. Siu N. Sliire Miţii Mheis Seio