Construction of Fixed Points of Asymptotically Nonexpansive Mappings in Uniformly Convex Hyperbolic Spaces

@article{Sipo2020ConstructionOF,
  title={Construction of Fixed Points of Asymptotically Nonexpansive Mappings in Uniformly Convex Hyperbolic Spaces},
  author={Andrei Sipoş},
  journal={Numerical Functional Analysis and Optimization},
  year={2020},
  volume={42},
  pages={696 - 711}
}
  • Andrei Sipoş
  • Published 10 August 2020
  • Mathematics
  • Numerical Functional Analysis and Optimization
Abstract Kohlenbach and Leuştean have shown in 2010 that any asymptotically nonexpansive self-mapping of a bounded nonempty UCW-hyperbolic space has a fixed point. In this paper, we adapt a construction due to Moloney in order to provide a sequence that converges strongly to such a fixed point. 
1 Citations
A proof of the asymptotic conjecture
In this paper we prove that if f is a self-mapping of a nonempty subset K of a normed space X that satisfies some mild conditions, then the minimal displacement of large iterations f n always

References

SHOWING 1-10 OF 30 REFERENCES
Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces
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
Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces
We propose the class of uniformly convex $W$-hyperbolic spaces with monotone modulus of uniform convexity ($UCW$-hyperbolic spaces for short) as an appropriate setting for the study of nonexpansive
A quadratic rate of asymptotic regularity for CAT(0)-spaces
Abstract In this paper we obtain a quadratic bound on the rate of asymptotic regularity for the Krasnoselski–Mann iterations of nonexpansive mappings in CAT(0)-spaces, whereas previous results
Construction of a fixed point for contractions in Banach space
A method for constructing fixed points of contractions in uniformly convex Banach spaces is developed. The fixed point obtained is the limit of one sequence that always converges (provided that a
A FIXED POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS
Let K be a subset of a Banach space X. A mapping F.K-+KI& said to be asymptotically nonexpansive if there exists a sequence {ki} of real numbers with £?-+1 as /'-►co such that WF'x—F'yW^kiWx—yW, yE
Nonexpansive iterations in hyperbolic spaces
ONE OF THE most active research areas in nonlinear functional analysis is the asymptotics of nonexpansive mappings. Most of the results, however, have been obtained in normed linear spaces. It is
An application of proof mining to nonlinear iterations
A quantitative mean ergodic theorem for uniformly convex Banach spaces
Abstract We provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of Tao of
Some fixed point theorems
Introduction. We wish to summarize here some new asymptotic fixed point theorems. By an asymptotic fixed point theorem we mean roughly a theorem in functional analysis in which the existence of fixed
On hyperbolic groups
Abstract We prove that a δ-hyperbolic group for δ < ½ is a free product F * G 1 * … * Gn where F is a free group of finite rank and each Gi is a finite group.
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