Fixed points of nonexpansive potential operators in Hilbert spaces

被引：5
|
作者：
Ricceri, Biagio [1 ]
机构：
[1] Univ Catania, Dept Math, I-95125 Catania, Italy
来源：
FIXED POINT THEORY AND APPLICATIONS | 2012年
关键词：
nonexpansive operator; potential operator; fixed point; well-posedness; NONLINEAR EIGENVALUE PROBLEMS; RICCERIS CONJECTURE;
D O I：
10.1186/1687-1812-2012-123
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we show the impact of certain general results by the author on the topic described in the title. Here is a sample: Let (X, <., .>) be a real Hilbert space and let T : X -> X be a nonexpansive potential operator. Then, the following alternative holds: either T has a fixed point, or, for each sphere S centered at 0, the restriction to S of the functional x -> integral(1)(0) < T(sx), x > ds has a unique global maximum towards which each maximizing sequence in S converges.
引用
收藏
页数：13
相关论文
共 50 条
  • [1] Fixed points of nonexpansive potential operators in Hilbert spaces
    Biagio Ricceri
    Fixed Point Theory and Applications, 2012
  • [2] Approximation of Fixed Points for Enriched Suzuki Nonexpansive Operators with an Application in Hilbert Spaces
    Ullah, Kifayat
    Ahmad, Junaid
    Arshad, Muhammad
    Ma, Zhenhua
    AXIOMS, 2022, 11 (01)
  • [3] Approximation of fixed points for nonexpansive semigroups in Hilbert spaces
    Yao, Yonghong
    Kang, Jung Im
    Cho, Yeol Je
    Liou, Yeong-Cheng
    FIXED POINT THEORY AND APPLICATIONS, 2013, : 1 - 11
  • [4] Approximation of fixed points for nonexpansive semigroups in Hilbert spaces
    Yonghong Yao
    Jung Im Kang
    Yeol Je Cho
    Yeong-Cheng Liou
    Fixed Point Theory and Applications, 2013
  • [5] Best approximations and fixed points of nonexpansive maps in Hilbert spaces
    Park, S
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1997, 18 (5-6) : 649 - 657
  • [6] Approximation of Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces
    Zhang, Dan
    Qin, Xiaolong
    Gu, Feng
    JOURNAL OF APPLIED MATHEMATICS, 2012,
  • [7] A hierarchical presentation of operators with fixed points on Hilbert spaces
    Crombez, G.
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2006, 27 (3-4) : 259 - 277
  • [8] PAIRS OF FIXED POINTS FOR A CLASS OF OPERATORS ON HILBERT SPACES
    Mokhtari, Abdelhak
    Saoudi, Kamel
    Repovs, Dusan D.
    FIXED POINT THEORY, 2024, 25 (02): : 667 - 676
  • [9] Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces
    Mainge, Paul-Emile
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (01) : 469 - 479
  • [10] On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces
    Suzuki, T
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (07) : 2133 - 2136
12345