Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings

Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings

In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions. Some numerical experiments are also given to support our main th...

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Veröffentlicht in:Mathematics (Basel) 2019-02, Vol.7 (2), p.167
Hauptverfasser: Cholamjiak, Prasit, Kesornprom, Suparat, Pholasa, Nattawut
Format: Artikel
Sprache:eng
Schlagworte:
Convergence
fixed point
Fixed points (mathematics)
Hilbert space
inverse strongly monotone mapping
maximal monotone operator
nonexpansive mappings
strong convergence
Theorems
weak convergence
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Beschreibung
Zusammenfassung:In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions. Some numerical experiments are also given to support our main theorem.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7020167