Fixed points of asymptotically regular mappings in spaces with uniformly normal structure

@inproceedings{GrnickiFixedPO,
  title={Fixed points of asymptotically regular mappings in spaces with uniformly normal structure},
  author={Jaros law G{\'o}rnicki}
}
It is proved that: for every Banach space X which has uniformly normal structure there exists a k > 1 with the property: if A is a nonempty bounded closed convex subset of X and T : A → A is an asymptotically regular mapping such that lim inf n→∞ |||T n ||| < k, where |||T ||| is the Lipschitz constant (norm) of T , then T has a fixed point in A. 

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-9 of 9 references

On uniformly normal structure

T. YuX.
Kexue Tongbao • 1988

A uniformly asymptotically regular mapping without fixed points

K. LinP.
Canad . Math . Bull . • 1987

Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure

E. Casini, E. Maluta
Nonlinear Anal . , TMA • 1985

Some properties of the characteristic convexity relating to fixed point theory

J. DowningD., B. Turett
Pacific J . Math . • 1983

Normal structure coefficients for Banach spaces

L. BynumW.
Pacific J . Math . • 1980

Fixed point theorem for nonexpansive mappings on Banach spaces with uniformly normal structure

A. GillespieA., B. WilliamsB.
Appl . Anal . • 1979

Nonexpansive mappings , asymptotic regularity and successive approximations

M. Edelstein, R. O’BrienC.
J . London Math . Soc . • 1978

The solution by iteration of nonlinear functional equations in Banach spaces

E. BrowderF., W. PetryshynV.
Bull . AMS • 1966

A fixed point theorem for asymptotically regular mappings , to appear

J. Górnicki
-1

Similar Papers

Loading similar papers…