An inertial-type algorithm for approximation of solutions of Hammerstein integral inclusions in Hilbert spaces
Open Access
- 29 March 2021
- journal article
- research article
- Published by Springer Science and Business Media LLC in Fixed Point Theory and Algorithms for Sciences and Engineering
- Vol. 2021 (1), 1-22
- https://doi.org/10.1186/s13663-021-00691-7
Abstract
Let H be a real Hilbert space. Let $F:H\rightarrow 2^{H}$ F : H → 2 H and $K:H\rightarrow 2^{H}$ K : H → 2 H be two maximal monotone and bounded operators. Suppose the Hammerstein inclusion $0\in u+KFu$ 0 ∈ u + K F u has a solution. We construct an inertial-type algorithm and show its strong convergence to a solution of the inclusion. As far as we know, this is the first inertial-type algorithm for Hammerstein inclusions in Hilbert spaces. We also give numerical examples to compare the new algorithm with some existing ones in the literature.Keywords
Funding Information
- African Development Bank
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