… firmly nonexpansive and piecewise affine operators within the convex envelope of the
training set. We show that this operator … T that are extended to the whole space via projection: …

… The notion of \(\alpha \)-firmly nonexpansive operator has also been considered in metric …
inequality for projections onto closed, convex sets. Then, in Sect. 3, we introduce \(\alpha \)-…

… this point a projection of x onto D. The mapping of a point x to its set of … type of regularity is
central to convergence of fixed point iterations. In a Banach space setting, firmly nonexpansive …

… Two well-known methods for CFP are the Sequential Projection Method (SPM) and the …
two particular choices of the separating operator S, which induce easily computable projections. …

… compared to the classical Parallel Projections Method (PPM). … projections, namely firmly
nonexpansive operators. … Clearly, xk belongs to U for all k, so that we may write xk = (xk,...,xk…

… ) and the subgradient projection method for solving nonlinear … operators and strongly
quasi-nonexpansive operators but it … of the projection operators in the string averaging procedure …

… -type nonexpansive mappings. Further, we use a new example of Reich–Suzuki-type
nonexpansive … scheme (1.6) converges strongly to a unique fixed point of \(\mathcalligra{U}\). …

… -type operators in Hilbert spaces as well as Banach spaces … We use \(P_{C}\) to denote the
metric projection from X onto C… Polynomial root finding is one of the oldest and most deeply …

… Since α-firmly nonexpansive operators in Hilbert spaces are important due to the related …
Let f(x) := PFix T (x) for x ∈ Rd, where PFix T denotes the metric projection onto Fix T. Then we …

… can not be used to the class of firmly type nonexpansive mappings. Theorem 1.3 gives a
positive answer to the Halpern open problem for the class of firmly nonexpansive mappings. …