Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces

Jarosław Górnicki

Commentationes Mathematicae Universitatis Carolinae (1989)

  • Volume: 030, Issue: 2, page 249-252
  • ISSN: 0010-2628

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Górnicki, Jarosław. "Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces." Commentationes Mathematicae Universitatis Carolinae 030.2 (1989): 249-252. <http://eudml.org/doc/17735>.

@article{Górnicki1989,
author = {Górnicki, Jarosław},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {asymptotic centre; uniformly convex Banach space; Opial's condition; asymptotically nonexpansive mapping; fixed point; weakly asymptotically regular},
language = {eng},
number = {2},
pages = {249-252},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces},
url = {http://eudml.org/doc/17735},
volume = {030},
year = {1989},
}

TY - JOUR
AU - Górnicki, Jarosław
TI - Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1989
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 030
IS - 2
SP - 249
EP - 252
LA - eng
KW - asymptotic centre; uniformly convex Banach space; Opial's condition; asymptotically nonexpansive mapping; fixed point; weakly asymptotically regular
UR - http://eudml.org/doc/17735
ER -

References

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  1. Bose S. C., Weak convergence to the fixed point of an asymptotically nonexpansive map, Proc. Amer. Math. Soc. 68 (1978), 305-308. (1978) Zbl0377.47037MR0493543
  2. Bose S. C., Laskar S. K., Fixed point theorems for certain class of mappings, Journ. Math. Phys. Sci. 19 (1985), 503-509. (1985) Zbl0613.47048MR0873691
  3. Browder F. E., Petryshyn W. V., The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 671-575. (1966) Zbl0138.08202MR0190745
  4. Goebel K., Kirk W. A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171-174. (1972) Zbl0256.47045MR0298500
  5. Goebel K., Reich S., Uniform convexity, Hyperbolic geometry and Nonexpansive mappings, Marcel Dekker, INC, New York, Basel, 1984. (1984) Zbl0537.46001MR0744194
  6. Hirano N., Nonlinear ergodic theorems and weak convergence theorems, J. Math. Soc. Japan 34 (1982), 35-46. (1982) Zbl0464.47041MR0639803
  7. Krüppel M., Mean ergodic theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces, [unpublished manuscript]. 
  8. Opial Z., Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597. (1967) Zbl0179.19902MR0211301

Citations in EuDML Documents

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  1. Zeqing Liu, Ravi P. Agarwal, Chi Feng, Shin Min Kang, Weak and strong convergence theorems of common fixed points for a pair of nonexpansive and asymptotically nonexpansive mappings
  2. Ronald Bruck, Tadeusz Kuczumow, Simeon Reich, Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property
  3. Kittipong Sitthikul, Satit Saejung, Convergence theorems for a finite family of nonexpansive and asymptotically nonexpansive mappings
  4. Daya Ram Sahu, Fixed points of demicontinuous nearly Lipschitzian mappings in Banach spaces

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