Abstract
AbstractWe survey recent results regarding genericity and porosity in fixed point theory. These results concern, inter alia, infinite products, nonexpansive mappings, approximate fixed points, contractive mappings, bounded linear regularity, set-valued mappings, holomorphic mappings and weak ergodic theorems. We consider both normed linear spaces and hyperbolic metric spaces.
Highlights
In this paper we use the concept of porosity which will enable us to obtain more refined results
We present a convergence theorem for infinite products governed by such elements, where we allow for computational errors
In our previous work [ ], Section . , pp., we studied a certain class of nonlinear self-mappings of a complete metric space endowed with a natural metric
Summary
In this paper we use the concept of porosity which will enable us to obtain more refined results. It follows from Banach’s fixed point theorem that every nonexpansive self-mapping of a bounded, closed and convex set in a Banach space has approximate fixed points.
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