The fixed point property for mappings admitting a center

Nonlinear Analysis, Theory, Methods and Applications

Volumn 66, Issue 6, 2007, Pages 1257-1274

  Garcia Falset J ^a   Llorens Fuster, E ^a   Prus, S ^b  

^a UNIVERSITY OF VALENCIA   (Spain)

^b MARIA CURIE SK ODOWSKA UNIVERSITY   (Poland)

Author keywords

Fixed points; Nearly strictly convex Banach spaces; Nonlinear operators

Indexed keywords

MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

FIXED POINTS; NEARLY STRICTLY CONVEX BANACH SPACES; NONLINEAR CONTINUOUS MAPPINGS; NONLINEAR OPERATORS;

MAPPING;

EID: 33845877981     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.01.016     Document Type: Article

References (27)

1. Alspach D.E. A fixed point free nonexpansive map. Proc. Amer. Math. Soc. 82 (1981) 423-424
2. Baillon J.B., and Schöneberg R. Asymptotic normal structure and fixed points of nonexpansive mappings. Proc. Amer. Math. Soc. 81 (1981) 257-264
3. Banas J. On drop property and nearly uniformly smooth Banach spaces. Nonlinear Anal. 14 11 (1990) 927-933
4. Barbu V. Nonlinear Semigroups and Differential Equations in Banach Spaces (1976), Noordhoff International Publishing
5. Bruck R.E. Properties of fixed-point sets of nonexpansive mappings in Banach spaces. Trans. Amer. Math. Soc. 179 (1973) 251-262
6. Cioranescu I. Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems (1990), Kluwer Academic Publishers
7. Daswish M.A. Weakly singular functional-integral equation in infinite dimensional Banach spaces. Appl. Math. Comput. 136 (2003) 123-129
8. Day M.M. Strict convexity and smoothness of normed spaces. Trans. Amer. Math. Soc. 78 (1955) 516-528
9. Díaz J.B., and Metcalf F.T. On the set of subsequential limit points of successive approximations. Trans. Amer. Math. Soc. 135 (1969) 459-485
10. Dotson W.G. On the Mann iterative process. Trans. Amer. Math. Soc. 149 (1970) 65-73
11. Garcia-Falset J. Fixed points for mappings with the range type condition. Houston J. Math. 28 (2002) 143-158
12. J. Garcia-Falset, S. Reich, Zeroes of accretive operators and the asymptotic behavior of nonlinear semigroups, Houston J. Math. (in press)
13. Goebel K., and Kirk W.A. Topics in Metric Fixed Point Theory (1990), Cambridge Univ. Press
14. Goebel K., Kirk W.A., and Shimi T. A fixed point theorem in uniformly convex spaces. Boll. Unione Mat. Ital. 7 (1973) 67-75
15. Goebel K., and Kirk W.A. Classical theory of nonexpansive mappings. In: Kirk W.A., and Sims B. (Eds). Handbook of Metric Fixed Point Theory (2001), Kluwer A. P.
16. Goebel K., and Sȩkowski T. The modulus of noncompact convexity. Ann. Univ. Mariae Curie-Sklodowska 29 38 (1984) 41-48
17. Goebel K., and Sims B. More on minimal invariant sets for nonexpansive mappings. Nonlinear Anal. 47 (2001) 2667-2681
18. Harandi A.A. A fixed point result in strictly convex Banach spaces. Acta Math. Hungar. 105 1-2 (2004) 139-143
19. Huff R.E. Banach spaces which are nearly uniformly convex. Rocky Mountain J. Math. 10 (1980) 743-749
20. Ishikawa S. Fixed points and iterations of nonexpansive mappings in Banach spaces. Proc. Amer. Math. Soc. 5 (1976) 65-71
21. Klee V. Some topological properties of convex sets. Trans. Amer. Math. Soc. 78 (1955) 30-45
22. Opial Z. Weak convergence of the sequence of succesive approximations for nonexpansive mappings. Bull. Amer. Math. Soc. 73 (1967) 595-597
23. Petryshyn W.V., and Williamson Jr. T.E. A necessary and sufficient condition for the convergence of a sequence of iterates for quasi nonexpansive mappings. Bull. Amer. Math. Soc. 78 6 (1972) 1027-1031
24. Rolewicz S. On drop property. Studia Math. 85 (1987) 27-35
25. Sine R. Remarks on the example of Alspach. Nonlinear Analysis and Applications. Lecture Notes in Pure and Appl. Math. vol. 80 (1982), Dekker, New York 237-241
26. M.A. Smyth, Aspects of the fixed point theory for some metrically defined maps, Ph.D. Dissertation, University of Newcastle, Australia, 1994
27. Troyanski S. On a property of the norm which is close to local uniform rotundity. Math. Ann. 271 (1985) 305-313