Weak and strong convergence theorems for \(m\)-generalized hybrid mappings in Hilbert spaces
Following \textit{P. Kocourek} et al. [Taiwanese J. Math. 14, No. 6, 2497--2511 (2010; Zbl 1226.47053)], the authors call a selfmap \(T\) of a closed convex subset \(C\) of a Hilbert space generalized hybrid if \[ \alpha\| Tx- Ty\|^2+ (1- \alpha)\| x-Ty\|^2\leq \beta\| Tx-y\|^2+ (1-\beta)\| x- y\|^2 \] for some \(\alpha,\beta\in\mathbb{R}\) and all \(x,y\in C\). A~generalization involving several constants \(\alpha_1,\dots, \alpha_m\), \(\beta_1,\dots, \beta_m\in\mathbb{R}\) and sums was introduced and studied by \textit{T. Maruyama} et al. [J. Nonlinear Convex Anal. 12, No. 1, 185--197 (2011; Zbl 1217.47098)]. In this paper, the authors give conditions for the weak or strong Ishikawa-type convergence for such maps.
scientific article; zbMATH DE number 6712690