| Title of Article |
On the strong convergence of sequences of Halpern type in Hilbert spaces |
| Date of Acceptance |
2 August 2018 |
| Journal |
| Title of Journal |
Optimization |
| Standard |
ISI |
| Institute of Journal |
Taylor & Francis |
| ISBN/ISSN |
|
| Volume |
|
| Issue |
67 |
| Month |
|
| Year of Publication |
2018 |
| Page |
1895-1922 |
| Abstract |
In this paper, we introduce a concept of $A$-sequences of Halpern type where $A$ is an averaging infinite matrix. If $A$ is the identity matrix, this notion become the well-know sequence generated by Halpern's iteration. A necessary and sufficient condition for the strong convergence of $A$-sequences of Halpern type is given whenever the matrix $A$ satisfies some certain concentrating conditions. This class of matrices includes two interesting classes of matrices considered by Combettes and Pennanen [J. Math. Anal. Appl. 2002;275:521--536]. We deduce all the convergence theorems studied by Cianciaruso et al. [Optimization. 2016;65:1259--1275] and Muglia et al. [J. Nonlinear Convex Anal. 2016;17:2071--2082] from our result. Moreover, these results are established under the weaker assumptions. We also show that the same conclusion remains true under a new condition. |
| Keyword |
fixed point; sequence of Halpern type; averaging matrix; concentrating matrix; L-hybrid mapping |
| Author |
|
| Reviewing Status |
มีผู้ประเมินอิสระ |
| Status |
ตีพิมพ์แล้ว |
| Level of Publication |
นานาชาติ |
| citation |
false |
| Part of thesis |
true |
| Attach file |
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| Citation |
0
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Publication
Journal Publication
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