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q -Uniformly Convex Metric Space and Its Application(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
1999年02期
Page:
93-96
Research Field:
Publishing date:

Info

Title:
q -Uniformly Convex Metric Space and Its Application
Author(s):
Shi Chuan
School of Sciences,NUST,Nanjing210094
Keywords:
systems eng ineering cont rol theory engineering mechanics f luid mechanics met ric space
PACS:
O177
DOI:
-
Abstract:
This paper put forw ard a concept of a class new convex met ric space, studied the relat ion betw een this space and Banach, Hardy, Sobelev, etc. space. A necessary and suf ficient condit ion w as gievn for a Banach space of this class convex metric space. It w as proved that H p , H r , p , L g, p spaces are all of this class convex met ric spaces when 1< p < +∞, g = max ( 2, p ) and r > 0. T his class convex metric space, w hich is just a new concept , may f ind its applicat ions in many reasarch areas such as system eng ineering , cont rol theory, eng ineering mechanics, fluid mechanics, etc. Moreover, a study of a class fixed point theorems is made in this space, these theorems extended the corresponding recent results.

References:

1 Takahashi W. A conv ex ity in metr ic space and non- ex pansive mappings. I Kodai Math Sem Rep,1970, 22: 142~ 149
2 Peus B, Smar zeweski R. Stro ngly unique best approx imationg and centers in uniformly convex spaces. J Math Anal Appl, 1987, 121: 10~ 21
3 Xu Hongkun. Ineg ualities in Banach space w ith applicat ions. Nonlinear Anal, 1991, 16: 1 127~1 138
4 Gaebel K. Convex ity balls and fix ed po int theorems for mapping s w ith nonexpansive square.Compositio Math, 1970, 22: 269~ 274
5 Goebel K, Zlotkiewiez E. Some fixed point theorems in Banach space. Coll Math, 1971, 23: 103~106
6 Gornicki J. Fix ed points of involut ions. Math Japannica, 1996, 43( 1) : 151~ 155

Memo

Memo:
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Last Update: 2013-03-29