A strong convergence theorem for maximal monotone operators in Banach spaces with applications
An algorithm is constructed to approximate a zero of a maximal monotone operator in a uniformly convex and uniformly smooth real Banach space. The sequence of the algorithm is proved to converge strongly to a zero of the maximal monotone map. In the case where the Banach space is a real Hilbert spac...
Veröffentlicht in: | Carpathian Journal of Mathematics. - Sinus Association. - 36(2020), 2, Seite 229-240 |
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1. Verfasser: | |
Weitere Verfasser: | , , |
Format: | Online-Aufsatz |
Sprache: | English |
Veröffentlicht: |
2020
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Zugriff auf das übergeordnete Werk: | Carpathian Journal of Mathematics |
Schlagworte: | Mathematics |
Zusammenfassung: | An algorithm is constructed to approximate a zero of a maximal monotone operator in a uniformly convex and uniformly smooth real Banach space. The sequence of the algorithm is proved to converge strongly to a zero of the maximal monotone map. In the case where the Banach space is a real Hilbert space, our theorem complements the celebrated proximal point algorithm of Martinet and Rockafellar. Furthermore, our convergence theorem is applied to approximate a solution of a Hammerstein integral equation in our general setting. Finally, numerical experiments are presented to illustrate the convergence of our algorithm. |
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ISSN: | 18434401 |