Iterative algorithms for common elements in fixed point sets and zero point sets with applications

In this study, Mann-type iterative process is considered for finding a common element in the fixed point set of strict pseudocontractions and in the zero point set of the operator which is the sum of inverse strongly- monotone operators and maximal monotone operators. Weak convergence theorems of co...

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Bibliographic Details
Published inFixed point theory and algorithms for sciences and engineering Vol. 2012; no. 1; pp. 1 - 14
Main Author Zhang, Mingliang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 22.02.2012
Springer Nature B.V
BioMed Central Ltd
Subjects
Analysis
Applications of Mathematics
Classification
Convergence
Differential Geometry
Fixed points (mathematics)
Hilbert space
Inverse
Iterative algorithms
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Operators
Theorems
Topology
nonexpansive mapping
strictly pseudocontractive mapping
variational inequality
inverse-strongly monotone mapping
equilibrium problem
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Summary:In this study, Mann-type iterative process is considered for finding a common element in the fixed point set of strict pseudocontractions and in the zero point set of the operator which is the sum of inverse strongly- monotone operators and maximal monotone operators. Weak convergence theorems of common elements are established in the framework of Hilbert spaces. Some applications of main results are also provided. AMS Subject Classification: 47H05; 47H09; 47J25; 90C33.
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ISSN:1687-1812
1687-1820
1687-1812
2730-5422
DOI:10.1186/1687-1812-2012-21