Effective Rates of Convergence for the Resolvents of Accretive Operators |
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Authors: | Angeliki Koutsoukou-Argyraki |
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Institution: | 1. Department of Mathematics, Technische Universit?t Darmstadt, Darmstadt, Germanykoutsoukou@mathematik.tu-darmstadt.de |
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Abstract: | 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/?-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 ?-expansivity, a notion introduced analogously here. |
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Keywords: | Accretive operator computable bound extraction proof mining rate of convergence resolvent |
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