Effective Rates of Convergence for the Resolvents of Accretive Operators
Angeliki Koutsoukou-Argyraki · Numerical Functional Analysis and Optimization · 2017
We extract explicit, computable, and highly uniform rates for the strong convergence of the resolvents of set-valued, m-accretive, and uniformly accretive at zero/ϕ-expansive operators on general real Banach spaces to the zero of each operator. This is achieved through proof mining on the proof of a theorem by García–Falset the motivation of which originates from a classical work by Reich. For the bound extraction we make use of a modulus of accretivity at zero, a notion introduced recently by Kohlenbach and the author, as well as a modulus of ϕ-expansivity, a notion introduced analogously here.