Probabilistic normed Riesz spaces

被引：0
作者：
Celaleddin Şenç.imen
Serpil Pehl.ivan
机构：
[1] Mehmet Akif Ersoy University,Department of Mathematics, Faculty of Arts and Sciences
[2] Süleyman Demirel University,Department of Mathematics, Faculty of Arts and Sciences
来源：
Acta Mathematica Sinica, English Series | 2012年 / 28卷
关键词：
Probabilistic normed Riesz space; probabilistic Banach lattice; order convergence; strong convergence; probabilistic norm Cauchy system; 46B42; 46S50;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, the concepts of probabilistic normed Riesz space and probabilistic Banach lattice are introduced, and their basic properties are studied. In this context, some continuity and convergence theorems are proved.
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页码：1401 / 1410
页数：9
相关论文
共 39 条
[1]  
Riesz F.(1928)Sur la décomposition des opérations linéaires Proc. Internat. Congress of Math. (Bologna) 3 143-148
[2]  
Freudenthal H.(1936)Teilweise geordnete Modulen Proc. Acad. Amsterdam 39 641-651
[3]  
Kantorovich L. V.(1937)Lineare halbgeordnete Raume Receueil Math. 2 121-168
[4]  
Kakutani S.(1941)Concrete representation of abstract (L)-spaces and the mean ergodic theorem Ann. Math. 42 523-537
[5]  
Luxemburg W. A. J.(1963)Notes on Banach function spaces I Indag. Math. 25 135-147
[6]  
Zaanen A. C.(1942)Representation of vector lattices J. Sci. Hiroshima Univ. A 12 17-35
[7]  
Maeda F.(1953)Linear topologies on semi-ordered linear spaces J. Fac. Sci. Hokkaido Univ. 12 87-104
[8]  
Ogasawara T.(1951)Probabilistic geometry Proc. Natl. Acad. Sci. USA 37 226-229
[9]  
Nakano H.(1985)On the theory of probabilistic metric spaces with applications Acta Mathematica Sinica (New Ser.) 1 366-377
[10]  
Menger K.(2008)A new contraction principle in Menger spaces Acta Mathematica Sinica, English Series 24 1379-1386
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