Vol.30 (2) 2008 — 4 articles found.

Remarks on some recent fixed point theorems

C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (2) 2008, pp. 56–63
Vol.30 (2) 2008
S.L. Singh; Rajendra Pant Details
(Received: 2007-10-09 )
(Received: 2007-10-09 )

S.L. Singh, Department of Mathematics, Gurukula Kangri University, Hardwar, India, and 21, Govind Nagar, Rishikesh 249201, India; email: vedicmri@gmail.com

Rajendra Pant, Department of Mathematics, S.P.R.C. Post Graduate College, Rohalki-Kishanpur, Hardwar, India; email: pant.rajendra@gmail.com


We obtain fixed and common point theorems generalizing fixed point theorems of W. A. Kirk and T. Suzuki for Banach and Meir–Keeler type asymptotic contractions.

Nous démontrons des théorèmes de points fixes et de points communs qui généralisent des théorèmes de points fixes du type de Banach et de Meir–Keeler pour les contractions asymptotiques.

Keywords: Banach contraction, Meir–Keeler type asymptotic contraction, asymptotic contraction, fixed point

AMS Subject Classification: Fixed-point and coincidence theorems 54H25

PDF(click to download): Remarks on some recent fixed point theorems

Diophantine inequality for equicharacteristic excellent Henselian local domains

C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (2) 2008, pp. 48–55
Vol.30 (2) 2008
Hirotada Ito; Shuzo Izumi Details
(Received: 2008-01-07 , Revised: 2008-03-30 )
(Received: 2008-01-07 , Revised: 2008-03-30 )

Hirotada Ito, Interdisciplinary Graduate School of Science and Engineering, Kinki University, Higashi-Osaka 577-8502, Japan; email: reen.salt.7125-8753@s6.dion.ne.jp

Shuzo Izumi, Department of Mathematics, Kinki University, Higashi-Osaka 577-8502, Japan; email: sizmsizm@gmail.com


G. Rond has proved a Diophantine type inequality for the field of quotients of the convergent or formal power series ring in multivariables. We generalize his theorem to the field of the quotients of an excellent Henselian local domain in equicharacteristic case.

G. Rond a démontré une inégalité de type diophantien pour le corps des quotients de séries convergentes (ou formelles) à plusieurs variables. On fait ici une généralisation de son théorème au corps des quotients d’un anneau local intégral henselien excellent dans le cas équi-caractéristique.

Keywords: Diophantine inequality, associated valuations, linear Artin approximation property, m-valuation

AMS Subject Classification: Valuation rings 13F30

PDF(click to download): Diophantine inequality for equicharacteristic excellent Henselian local domains

Factorization of an indefinite convection-diffusion operator

C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (2) 2008, pp. 40–47
Vol.30 (2) 2008
Marina Chugunova; Vladimir Strauss Details
(Received: 2008-02-04 )
(Received: 2008-02-04 )

Marina Chugunova, Department of Mathematics. University of Toronto, Toronto, Ontario M5S 2E4 Canada; email: chugunom@math.toronto.edu

Vladimir Strauss, Department of Mathematics, Universidad Simon Bolıvar, Caracas 1080, Venezuela; email: str@usb.ve


We prove that a certain non-self-adjoint differential operator admits factorization, and we apply this new representation of the operator to explicitly construct its domain. We also show that the operator is J-self-adjoint in a Krein space.

On montre qu’un certain opérateur non autoadjoint admet une factorisation et, on utilise cette représentation pour construire explicitement son domaine. On montre aussi que cet opérateur est J-autoadjoint dans un espace de Krein.

Keywords: J-self-adjoint, Krein space, backward-forward heat equation, factorization, fluid mechanics

AMS Subject Classification: Operators belonging to operator ideals (nuclear; $p$-summing; in the Schatten-von Neumann classes; etc.) 47B10

PDF(click to download): Factorization of an indefinite convection-diffusion operator

Hypergroups with unique $\alpha$-means

C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (2) 2008, pp. 33–39
Vol.30 (2) 2008
Ahmadreza Azimifard Details
(Received: 2007-08-18 )
(Received: 2007-08-18 )

Ahmadreza Azimifard, Dietlinden Strasse 16, 80802 Munchen, Bayern, Deutschland; email: azimifard@hotmail.de


Let \(K\) be a commutative hypergroup and \(\alpha\in \widehat{K}\). We show that \(K\) is \(\alpha\)-amenable with the unique \(\alpha\)-mean \(m_\alpha\) if and only if \(m_\alpha \in L^1(K) \cap L^2(K)\) and \(\alpha\) is isolated in \(\widehat{K}\). In contrast to the case of amenable noncompact locally compact groups, examples of polynomial hypergroups with unique \(\alpha\)-means (\(\alpha \not= 1\)) are given. Further examples emphasize that the \(\alpha\)-amenability of hypergroups depends heavily on the asymptotic behavior of Haar measures and characters.

Soit \(K\) un hypergroupe commutatif et \(\alpha\in \widehat{K}\). Nous montrons que \(K\) est \(\alpha\)-moyennable avec unicité de l’\(\alpha\)-moyenne \(m_\alpha\) si et seulement si \(m_\alpha \in L^1(K) \cap L^2(K)\) et \(\alpha\) est isolé dans \(\widehat{K}\). Contrairement au cas des groupes moyennables localement compacts mais non compacts, des exemples d’hyper-groupes polynomiaux avec unicité des \(\alpha\)-moyennes (\(\alpha \not= 1\)) sont donnés. Nous montrons à l’aide d’autres examples que l’\(\alpha\)-moyennabilité des hypergroupes dépend fortement de leurs mesures de Haar ainsi que du comportement des caractères.

Keywords: hypergroups of Nevaei classes, orthogonal polynomial hypergroups, α-amenable hypergroups

AMS Subject Classification: Hypergroups 43A62

PDF(click to download): Hypergroups with unique $alpha$-means

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