$$\alpha $$-Firmly nonexpansive operators on metric spaces

Abstract We extend to p -uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted an appropriate generalization single-valued, pointwise averaged mappings. Our main contribution establishing a calculus for these mappings spaces, showing particular how property preserved under compositions and combinations. central importance splitting algorithms that are built by such combinations compositions, reduces convergence simply verifying individual components have required regularity at points algorithms. differs what can be found previous literature assumptions only with respect points. Indeed we show that, if mapping nonexpansive all cluster points, then fact sequence follows. Additionally, provide quantitative on notion gauge metric subregularity, which necessary quantifiable estimates. allows one first time prove tremendous variety curvature bounded above.