Strong convergence theorems for maximal monotone operators with nonspreading mappings in a Hilbert space (Q1938332)

Summary: We prove strong convergence theorems for finding a common element of the set of fixed points of a nonspreading mapping \(T\) and the zero sets of a maximal monotone mapping and an \(\alpha\)-inverse strongly monotone mapping in a Hilbert space. \textit{H. Manaka} and \textit{W. Takahashi} [Cubo 13, No.~1, 11--24 (2011; Zbl 1247.47070)] proved weak convergence theorems for maximal monotone operators with nonspreading mappings in a Hilbert space; we introduce new iterative algorithms and get some strong convergence theorems for maximal monotone operators with nonspreading mappings in a Hilbert space.