Fixed point theorems and convergence theorems for some generalized nonexpansive mappings

Journal of Mathematical Analysis and Applications

Volumn 340, Issue 2, 2008, Pages 1088-1095

  Suzuki, Tomonari ^a  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Convergence theorem; Fixed point; Nonexpansive mapping

Indexed keywords

EID: 38049041447     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.09.023     Document Type: Article

References (21)

1. Baillon J.B. Quelques aspects de la théorie des points fixes dans les espaces de Banach. I, II. Séminaire d'Analyse Fonctionnelle (1978-1979), vols. 7-8 (1979), École Polytech., Palaiseau 45 pp. (in French)
2. Browder F.E. Fixed-point theorems for noncompact mappings in Hilbert space. Proc. Natl. Acad. Sci. USA 53 (1965) 1272-1276
3. Browder F.E. Nonexpansive nonlinear operators in a Banach space. Proc. Natl. Acad. Sci. USA 54 (1965) 1041-1044
4. Connell E.H. Properties of fixed point spaces. Proc. Amer. Math. Soc. 10 (1959) 974-979
5. Diaz J.B., and Metcalf F.T. On the structure of the set of subsequential limit points of successive approximations. Bull. Amer. Math. Soc. 73 (1967) 516-519
6. van Dulst D. Equivalent norms and the fixed point property for nonexpansive mappings. J. London Math. Soc. 25 (1982) 139-144
7. Edelstein M., and O'Brien R.C. Nonexpansive mappings, asymptotic regularity and successive approximations. J. London Math. Soc. 17 (1978) 547-554
8. Goebel K., and Kirk W.A. Iteration processes for nonexpansive mappings. Contemp. Math. 21 (1983) 115-123
9. Goebel K., and Kirk W.A. Topics in Metric Fixed Point Theory. Cambridge Stud. Adv. Math. vol. 28 (1990), Cambridge Univ. Press
10. Göhde D. Zum Prinzip def kontraktiven Abbildung. Math. Nachr. 30 (1965) 251-258
11. Gossez J.-P., and Lami Dozo E. Some geometric properties related to the fixed point theory for nonexpansive mappings. Pacific J. Math. 40 (1972) 565-573
12. Ishikawa S. Fixed points and iteration of a nonexpansive mapping in a Banach space. Proc. Amer. Math. Soc. 59 (1976) 65-71
13. Kirk W.A. A fixed point theorem for mappings which do not increase distances. Amer. Math. Monthly 72 (1965) 1004-1006
14. Kirk W.A. Caristi's fixed point theorem and metric convexity. Colloq. Math. 36 (1976) 81-86
15. Opial Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Amer. Math. Soc. 73 (1967) 591-597
16. Prus S. Geometrical background of metric fixed point theory. In: Kirk W.A., and Sims B. (Eds). Handbook of Metric Fixed Point Theory (2001), Kluwer Academic Publishers, Dordrecht 93-132
17. Subrahmanyam P.V. Completeness and fixed-points. Monatsh. Math. 80 (1975) 325-330
18. Suzuki T. Krasnoselskii and Mann's type sequences and Ishikawa's strong convergence theorem. In: Takahashi W., and Tanaka T. (Eds). Proceedings of the Third International Conference on Nonlinear Analysis and Convex Analysis (2004), Yokohama Publishers 527-539
19. Suzuki T. Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces. Fixed Point Theory Appl. 2005 (2005) 103-123
20. Suzuki T. Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals. J. Math. Anal. Appl. 305 (2005) 227-239
21. T. Suzuki, A generalized Banach contraction principle which characterizes metric completeness, Proc. Amer. Math. Soc., in press