Journal
COMPUTATIONAL & APPLIED MATHEMATICS
Volume 37, Issue 5, Pages 5750-5774Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-018-0661-z
Keywords
Inertial method; Inclusion problem; Maximal monotone operator; Forward-backward algorithm; Quasi-nonexpansive mapping; 47J22; 47H04; 47H05; 47H10
Categories
Funding
- Thailand Research Fund [MRG6080105]
- University of Phayao
- Chiang Mai University
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In this work, we propose a modified inertial and forward-backward splitting method for solving the fixed point problem of a quasi-nonexpansive multivalued mapping and the inclusion problem. Then, we establish the weak convergence theorem of the proposed method. The strongly convergent theorem is also established under suitable assumptions in Hilbert spaces using the shrinking projection method. Some preliminary numerical experiments are tested to illustrate the advantage performance of our methods.
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