Generic convergence of iterates for a class of nonlinear mappings (Q2388425)

Let \(K\) be a nonempty, bounded, closed and convex subset of a Banach space \(X\). It is proved that a class of continuous self-mappings of \(K\) has a subclass \(\mathcal F\) with the property that the complement of \(\mathcal F\) is \(\sigma\)-porous and each element \(A\in \mathcal F\) has a unique fixed point \(x_A\) such that \(\{A^n\}\) converges uniformly on \(K\) to \(x_A\). Here the concept of porosity is due to \textit{F. S. De Blasi} and \textit{J. Myjak} [C. R. Acad. Sci., Paris, Sér. I 308, No.~2, 51--54 (1989; Zbl 0657.47053)].