An inertial-type algorithm for approximation of solutions of Hammerstein integral inclusions in Hilbert spaces

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Abstract LetHbe a real Hilbert space. Let $F:H\rightarrow 2^{H}$ F:H→2H and $K:H\rightarrow 2^{H}$ K:H→2H be two maximal monotone and bounded operators. Suppose the Hammerstein inclusion $0\in u+KFu$ 0∈u+KFu 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.

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