Approximating common fixed points of averaged self-mappings with applications to the split feasibility problem and maximal monotone operators in Hilbert spaces

In this paper, a modified proximal point algorithm for finding common fixed points of averaged self-mappings in Hilbert spaces is introduced and a strong convergence theorem associated with it is proved. As a consequence, we apply it to study the split feasibility problem, the zero point problem of...

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Bibliographic Details
Published inFixed point theory and applications (Hindawi Publishing Corporation) Vol. 2013; no. 1; p. 190
Main Authors Huang, Young-Ye, Hong, Chung-Chien
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 19.07.2013
BioMed Central Ltd
Subjects
Analysis
Applications of Mathematics
Differential Geometry
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Topology
firmly nonexpansive mapping
maximal monotone operator
split feasibility problem
minimization problem
averaged mapping
equilibrium problem
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Summary:In this paper, a modified proximal point algorithm for finding common fixed points of averaged self-mappings in Hilbert spaces is introduced and a strong convergence theorem associated with it is proved. As a consequence, we apply it to study the split feasibility problem, the zero point problem of maximal monotone operators, the minimization problem and the equilibrium problem, and to show that the unique minimum norm solution can be obtained through our algorithm for each of the aforementioned problems. Our results generalize and unify many results that occur in the literature. MSC: 47H10, 47J25, 68W25.
ISSN:1687-1812
1687-1812
DOI:10.1186/1687-1812-2013-190