[1]张 慧.广义模糊p-伪范数与局部半凸I-拓扑向量空间(英文)[J].南京师大学报(自然科学版),2008,31(01):8-14.
　Zhang Hui,Fang Jinxuan.Generalized Fuzzy p-Pseudonorm and Locally Semi-Convex I-Topological Vector Spaces[J].Journal of Nanjing Normal University(Natural Science Edition),2008,31(01):8-14.
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广义模糊p-伪范数与局部半凸I-拓扑向量空间(英文)()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第31卷
期数:
2008年01期
页码:
8-14
栏目:
数学
出版日期:
2008-03-30

文章信息/Info

Title:
Generalized Fuzzy p-Pseudonorm and Locally Semi-Convex I-Topological Vector Spaces
作者:
张 慧1;  2;  方锦暄1
( 1. 南京师范大学数学与计算机科学学院, 江苏南京210097 )
( 2. 安徽师范大学数学系, 安徽芜湖241000)
Author(s):
Zhang Hui1; 2; Fang Jinxuan1
( 1. S chool ofM athem atics and C ompu ter Science, N an jing Norm alUn iversity, Nan jing 210097, Ch ina)
( 2. Departm en t ofM athem atics, Anhu iN orm alUn ivers ity, W uhu 241000, Ch ina )
关键词:
半凸模糊集;  局部半凸I-拓扑向量空间;  广义模糊p-伪范数
Keywords:
sem -i conv ex fuzzy set;  locally sem -i convex I- topo log ica l vecto r space;  genera lized fuzzy p - pseudono rm
分类号:
O189.13
摘要:
给出局部半凸I-拓扑向量空间的一个新定义,并重新命名"局部半凸模糊拓扑线性空间"为"(QL)-型局部半凸I-拓扑向量空间",研究这两种定义之间的关系,引入广义模糊p-伪范数的概念,证明每个局部半凸I-拓扑向量空间可通过一族广义模糊p-伪范数来刻画.
Abstract:
In th is paper, we g ive a new de finition of locally sem -i convex I- topo log ica l v ec tor spaces and renam e lo ca lly sem -i convex fuzzy topo log ica l linear spaces as locally sem -i convex I- topo log ica l vecto r spaces o f (QL ) - type. The relation be tw een these two defin itions is studied. W e introduce the no tion o f genera lized fuzzy p - pseudono rm, and prove tha t ev ery locally sem -i convex I- vector topo logy can be determ ined by a fam ily o f genera lized fuzzy p- pseudonorm s

参考文献/References:

[ 1] Ka tsaras A K. Fuzzy topo log ica l vec to r spaces I[ J]. Fuzzy Sets and System s, 1981, 6( 1): 85-95.
[ 2] Ka tsaras A K. Fuzzy topo log ica l vec to r spaces II[ J] . Fuzzy Sets and System s, 1984, 12( 2): 143-154.
[ 3] Fang Jinxuan. On local bases o f fuzzy topo log ical vector spaces[ J]. Fuzzy Se ts and System s, 1997, 87( 3): 341-347.
[ 4] Fang Jinxuan, Y an Conghua. Sem -i convex ity and fuzzy topolog ica l linear space[ J]. J Nan jing No rm al Un iversity: Natural Sc ience Edition, 1992, 15( 3): 21-26.
[ 5] K rishna S V, Sarma K K M. Fuzzy topo log ica l vector space- topo log ica l generation and normability[ J]. Fuzzy Sets and System s, 1991, 41( 1) : 89-99.
[ 6] K rishna S V, Sa rma K K M. Fuzzy continu ity of linearm aps on vector spaces[ J]. Fuzzy Sets and System s, 1992, 45( 3): 341-354.
[ 7] K rishna S V, Sa rma K K M. Separations o f fuzzy linea r spaces[ J]. Fuzzy Sets and System s, 1994, 63( 2): 207-217.
[ 8] W u Congx in, Fang Jinxuan. Rede fine of fuzzy topolog ical vector space[ J]. Sc ience Exp loration ( Ch ina), 1982, 2( 4): 113- 116.
[ 9] W u Congx in, Fang Jinxuan. QL-type fuzzy topo log ica l vecto r spaces[ J]. Ch inese AnnM ath, 1985, 6A( 3): 355-364. ( in Chinese) .
[ 10] W u Congx in, Fang Jinxuan. Fuzzy gene ra liza tion o f Ko lmogoroff ’s theo rem [ J]. J H arb in Institute Techno logy, 1984, 10( 1) : 1-7.
[ 11] Wu Congx in, Fang Jinxuan. Boundedness and locally bounded fuzzy topo log ical vec to r spaces[ J] . Fuzzy M ath ( China), 1985, 5( 4): 80-89.
[ 12] Wu Congx in, Gao Yaguang. Loca lP-convex ity o f fuzzy topo log ica l linear space and quasiP-no rm ed fuzzy topo log ical linear space[ J]. JH a rbin Institute o f Techno logy, 1986, 12( 4): 117-118.
[ 13] Wu Congx in, L i Jianhua. Convex ity and fuzzy topo log ical vector spaces[ J]. Sc ience Exploration ( China) , 1984, 4( 1): 1- 4.
[ 14] Wu Congx in, L i Jianhua. Convex ity and fuzzy topo log ica l vec to r spaces Ò [ J] . K exue Tongbao ( Ch ina ), 1985, 30( 9): 796.
[ 15] W u Congx in, Duan Yanzheng. On the inductive lim it of fuzzy topo log ica l v ector spaces[ J]. Fuzzy System s andM ath ( Ch-i na) , 1987, 1( 1): 35-44.
[ 16] HÊ hle U, Rodabaugh S E. M athema tics of Fuzzy Sets: Log ic, Topo logy, andM easure Theo ry [M ] / / The H andbooks o f Fuzzy Sets Ser ies. Dordrecht: K luw er Academ ic Publishers, 1999.
[ 17] Pu Paom ing, Liu Y ingm ing. Fuzzy topo logy I, ne ighborhood struc tures o f a fuzzy po in ts andM oo re-Sm ith conv ergence[ J]. JM ath Anal App,l 1980, 76( 2): 571-599.
[ 18] Zhang Hu ,i Fang Jinxuan. On loca lly convex I- topo log ical vector spaces [ J] . Fuzzy Se ts and System s, 2006, 157( 14): 1 995-2 002.

备注/Memo

备注/Memo:
Foundation item: Supported by the NNSF ( 10671094 ) , th e Specialized R esearch Fund for the Doctor Program ofH igher E ducation of Ch ina
( 20060319001 ) and the NSF for the H igher E du cation ofAnhu i( KJ2008B242) .
Biography: Zhang H u,i fem ale, born in 1976, doctor, m ajored in th e fun ct ion al analys is and fuzzy mathem atics. E-m ail: zh9907084@ sohu. com
Corresponding autho r: Fang J inxuan, born in 1943, p rofessor, m ajored in the functional ana lysis and fuzzy mathem atics. E-m ail:jxfang@ n jnu.
edu. cn
更新日期/Last Update: 2013-05-05