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Further investigation into split common fixed point problem for demicontractive operators
- Source :
- Acta Mathematica Sinica, English Series. 32:1357-1376
- Publication Year :
- 2016
- Publisher :
- Springer Science and Business Media LLC, 2016.
-
Abstract
- Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point problem of demicontractive mappings in a real Hilbert space. So many authors have used algorithms involving the operator norm for solving split common fixed point problem, but as widely known the computation of these algorithms may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some applications of our result and numerical example at the end of the paper.
- Subjects :
- Mathematical optimization
Sequence
Iterative method
Applied Mathematics
General Mathematics
Computation
010102 general mathematics
Hilbert space
01 natural sciences
010101 applied mathematics
symbols.namesake
Convergence (routing)
symbols
Common fixed point
0101 mathematics
Operator norm
Mathematics
Subjects
Details
- ISSN :
- 14397617 and 14398516
- Volume :
- 32
- Database :
- OpenAIRE
- Journal :
- Acta Mathematica Sinica, English Series
- Accession number :
- edsair.doi...........24054fe314e8e414fe30beb026f27107