Conical averagedness and convergence analysis of fixed point algorithms

We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis fixed point algorithms. Various properties conically are systematically investigated, particular, stability under relaxations, convex combinations compositions. derive averagedness resolvents generalized monotone operators. These then utilized order to analyze proximal algorithm, forward–backward adaptive Douglas–Rachford algorithm. Our unifies, improves casts new light on recent studies these topics.