An ultrafilter approach to locally almost nonexpansive maps

Nonlinear Analysis, Theory, Methods and Applications

Volumn 63, Issue 5-7, 2005, Pages

  Kirk, W A ^a   Sims, Brailey ^b  

^a UNIVERSITY OF IOWA   (United States)

^b UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

Banach space ultrapowers; Demiclosedness; Fixed points; Locally almost nonexpansive mappings; The Opial property

Indexed keywords

MAPPING; MAPS;

BANACH SPACE ULTRAPOWERS; DEMICLOSEDNESS; FIXED POINTS; LOCALLY ALMOST NONEXPENSIVE MAPPINGS; THE OPIAL PROPERTY;

SET THEORY;

EID: 28044453914     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.10.017     Document Type: Conference Paper

References (12)

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3. F. Browder Semicontractive and semiaccretive nonlinear mappings in Banach spaces Bull. Amer. Math. Soc. 74 1968 660 665
4. G. Darbo Punti uniti in trasformazioni a condiminio non compatto Rend. Sem. Mat. Univ. Padova 24 1955 84 92
5. K. Goebel, and W.A. Kirk Topics in Metric Fixed Point Theory 1990 Cambridge University Press Cambridge
6. M.A. Khamsi, and B. Sims Ultra-methods in metric fixed point theory W.A. Kirk B. Sims Handbook of Metric Fixed Point Theory 2001 Kluwer Academic Publishers Dordrecht 177 199
7. W.A. Kirk Mappings of generalized contractive type J. Math. Anal. Appl. 32 1970 567 572
8. W.A. Kirk, C. Martínez Yañez, and S.S. Shin Asymptotically nonexpansive mappings Nonlinear Anal. 33 1998 1 12
9. R. Nussbaum Degree theory for local condensing mappings J. Math. Anal. Appl. 37 1972 741 766
10. Z. Opial Weak convergence of the sequence of successive approximations for nonexpansive mappings Bull. Amer. Math. Soc. 73 1967 595 597
11. B. Sims, "Ultra"-Techniques in Banach Space Theory, Queen's Papers in Pure and Applied Mathematics, No. 160, Queen's University, Kingston, Ontario, 1982.
12. B. Sims, and H.K. Xu Locally almost nonexpansive mappings Comm. Appl. Nonlinear Anal. 8 2001 81 88