Existence theorems for monotone operators in reflexive Banach spaces

被引：0

作者：

Matsushita, Shin-Ya ^{[1
]}

Takahashi, Wataru

机构：

[1] Matsue Natl Coll Technol, Dept Informat Engn, Matsue, Shimane 6908518, Japan

[2] Tokyo Inst Technol, Dept Math & Comp Sci, Meguro Ku, Tokyo 1528552, Japan

来源：

ARCHIV DER MATHEMATIK | 2007年 / 89卷 / 03期

关键词：

monotone operators; existence of zeros; metric projection; duality mapping; fixed point; nonexpansive mapping;

D O I：

10.1007/s00013-007-2070-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we obtain an existence theorem for single-valued monotone operators in a reflexive Banach space. Using this result, we prove a fixed point theorem for nonexpansive mappings in a Hilbert space and an existence theorem for maximal monotone operators in a Banach space.

引用

页码：254 / 265

页数：12

共 50 条

[1] Existence theorems for monotone operators in reflexive Banach spaces
Shin-Ya Matsushita
Wataru Takahashi
[J]. Archiv der Mathematik, 2007, 89 : 254 - 265
[2] On the existence of zeros of monotone operators in reflexive Banach spaces
Matsushita, Shin-ya
Takahashi, Wataru
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (02) : 1354 - 1364
[3] EXISTENCE RESULTS FOR MULTIVALUED OPERATORS OF MONOTONE TYPE IN REFLEXIVE BANACH SPACES
Adhikari, Dhruba R.
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, : 1 - 10
[4] EXISTENCE AND PERTURBATION THEOREMS FOR NONLINEAR MAXIMAL MONOTONE OPERATORS IN BANACH SPACES
BROWDER, FE
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (03) : 322 - &
[5] ZERO THEOREMS OF ACCRETIVE OPERATORS IN REFLEXIVE BANACH SPACES
Yang, S.
[J]. JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2013,
[6] On the connection between the existence of zeros and the asymptotic behavior of resolvents of maximal monotone operators in reflexive Banach spaces
Kartsatos, AG
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 350 (10) : 3967 - 3987
[7] Strong convergence theorems for maximal monotone operators in Banach spaces
Ceng, L. C.
Schaible, S.
Yao, J. C.
[J]. OPTIMIZATION, 2010, 59 (06) : 807 - 819
[8] Composite iterative schemes for maximal monotone operators in reflexive Banach spaces
Prasit Cholamjiak
Yeol Je Cho
Suthep Suantai
[J]. Fixed Point Theory and Applications, 2011
[9] The sum theorem for maximal monotone operators in reflexive Banach spaces revisited
Voisei, Mircea D.
[J]. STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2021, 66 (01): : 123 - 126
[10] Composite iterative schemes for maximal monotone operators in reflexive Banach spaces
Cholamjiak, Prasit
Cho, Yeol Je
Suantai, Suthep
[J]. FIXED POINT THEORY AND APPLICATIONS, 2011,

← 1 2 3 4 5 →