Scientiae Mathematicae Japonicae

STONE-WEIERSTRASS TYPE THEOREMS FOR ALGEBRAS CONTAINING CONTINUOUS UNBOUNDED FUNCTIONS

Mati Abel, Jorma Arhippainen, Jukka Kauppi

2010 Volume 71 Issue 1 Pages 1-10
Published: 2010
Released on J-STAGE: August 30, 2019

DOIhttps://doi.org/10.32219/isms.71.1_1

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CI-ALGEBRAS

BIAO LONG MENG

2010 Volume 71 Issue 1 Pages 11-17
Published: 2010
Released on J-STAGE: August 30, 2019

DOIhttps://doi.org/10.32219/isms.71.1_11

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In this paper we introduce the notion of CI -algebras as a generalization of BE-algebras and dual BCK/BCI/BCH-algebras, we investigate its elementary properties. Relations of CI-algebras and BE-algebras are discussed. Finally we prove that in transitive BE-algebras, the notion of ideals is equivalent to one of filters.

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THE HIAI-PETZ GEODESIC FOR STRONGLY CONVEX NORM IS THE UNIQUE SHORTEST PATH

Jun Ichi Fujii

2010 Volume 71 Issue 1 Pages 19-26
Published: 2010
Released on J-STAGE: August 30, 2019

DOIhttps://doi.org/10.32219/isms.71.1_19

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Recently Hiai-Petz [7] introduced two types of interesting geometries of positive-definite matrices whose geodesics are paths of operator means and then the author [5] showed these geometries have Finsler structures for all unitarily invariant norms. Though the geodesic is of the shortest length between fixed two matrices, the shortest paths are not unique in general as pointed out in [7]. In this paper, we show that their geodesic is the unique shortest path in each Hiai-Petz geometry for all strongly convex unitarily invariant norms. As counter examples, we show that this uniqueness is false for Ky Fan norms.

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GIAMBELLI’S FORMULA AND THE BEST CONSTANT OF SOBOLEV INEQUALITY IN ONE DIMENSIONAL EUCLIDEAN SPACE

Yoshinori Kametaka, Atsushi Nagai, Kohtaro Watanabe, Kazuo Takemura, H ...

2010 Volume 71 Issue 1 Pages 27-41
Published: 2010
Released on J-STAGE: August 30, 2019

DOIhttps://doi.org/10.32219/isms.71.1_27

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The best constant of Sobolev inequality associated with 2N-th order Hurwitz-type differential operator is computed. Giambelli’s formula which appears in representation theory of finite groups plays an important role.

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ON π GENERALIZED β-CLOSED SETS IN TOPOLOGICAL SPACES II

S.C. Arora, Sanjay Tahiliani, H. Maki

2010 Volume 71 Issue 1 Pages 43-54
Published: 2010
Released on J-STAGE: August 30, 2019

DOIhttps://doi.org/10.32219/isms.71.1_43

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The concept of πgβ-closed sets is introduced and investigated by Tahiliani [12] earlier. In the present paper we investigate some more properties of πgβ-closed sets. Their relations in group theory and digital line are investigated.

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ON SOME MAPS CONCERNING gp-CLOSED SETS AND RELATED ROUPS

Arafa A. Nasef, Haruo Maki

2010 Volume 71 Issue 1 Pages 55-81
Published: 2010
Released on J-STAGE: August 30, 2019

DOIhttps://doi.org/10.32219/isms.71.1_55

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In the present paper we first introduce three classes of maps called approximately s.M-precontinuity, approximately s.M-preclosedness and contra-preirresoluteness. We obtain their basic properties and their relationships with other types of mappings between topological spaces. Finally, we construct and investigate some groups of some mappings corresponding to a topological space. We show some group structures for a subspace of the digital line and the digital plane.

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FIXED POINTS FOR MULTIVALUED CONTRACTIONS WITH RESPECT TO A w-DISTANCE.

JESUS GARCIA FALSET, LILIANA GURAN, ENRIQUE LLORENS-FUSTER

2010 Volume 71 Issue 1 Pages 83-91
Published: 2010
Released on J-STAGE: August 30, 2019

DOIhttps://doi.org/10.32219/isms.71.1_83

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The aim of this paper is to obtain a generalization of some well known fixed point theorems for multivalued mappings of contractive type in the framework of complete metric spaces, by using the concept of w-distance.

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ORDER AMONG POWER MEANS OF POSITIVE OPERATORS, II

Jadranka Mi´ci´c, Josip Peˇcari´c

2010 Volume 71 Issue 1 Pages 93-109
Published: 2010
Released on J-STAGE: August 30, 2019

DOIhttps://doi.org/10.32219/isms.71.1_93

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As a continuation of our previous research [Sci. Math. Japon. 61 (2005), 25–46.], we discuss order among power means of positive operators with a unital ntuple of positive linear maps.

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