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

Fixexd point theory and applications

article

Bello, A. U.¹  Omojola, M. T.¹  Yahaya, J.³ 

[1] African University of Science and Technology;Federal University Dutsinma;Ahmadu Bello University

关键词: Maximal monotone maps;    Hammerstein integral inclusion;    Inertial algorithm;   

DOI  :  10.1186/s13663-021-00691-7

来源: SpringerOpen

【 摘 要 】

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

【 授权许可】

Unknown