Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

Abstract

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed point theory of such mappings.

to appear in Journal of the European Mathematical Society; minor revision

References in corpus (1)

• Norm convergence of multiple ergodic averages for commuting transformations

Cited by in corpus (2)

• Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces
• A quantitative Mean Ergodic Theorem for uniformly convex Banach spaces