Quasi-asymptotic contractions, set-valued dynamic systems, uniqueness of endpoints and generalized pseudodistances in uniform spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 70, Issue 2, 2009, Pages 1059-1068

  Włodarczyk, Kazimierz ^a   Plebaniak, Robert ^a  

^a UNIVERSITY OF LODZ   (Poland)

Author keywords

Closed map; Dynamic process; Family of generalized pseudodistances; Generalized sequence of iterations; Locally convex space; Metric space; Quasi asymptotic contraction; Set valued dynamic system; Uniform space; Uniqueness of endpoint; Upper semicontinuous map

Indexed keywords

ASYMPTOTIC ANALYSIS; DYNAMIC PROGRAMMING; DYNAMICAL SYSTEMS; MAPS; SCHRODINGER EQUATION; SET THEORY; SHRINKAGE;

CLOSED MAP; DYNAMIC PROCESS; FAMILY OF GENERALIZED PSEUDODISTANCES; GENERALIZED SEQUENCE OF ITERATIONS; LOCALLY CONVEX SPACE; METRIC SPACE; QUASI-ASYMPTOTIC CONTRACTION; SET-VALUED DYNAMIC SYSTEM; UNIFORM SPACE; UNIQUENESS OF ENDPOINT; UPPER SEMICONTINUOUS MAP;

TOPOLOGY;

EID: 56049083318     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2008.01.032     Document Type: Article

References (28)

1. Agarwal R.P., O'Regan D., and Shahzad N. Fixed point theory for generalized contractive maps of Meir-Keeler type. Math. Nachr. 276 (2004) 3-22
2. Arandelovic I.A. Note on asymptotic contractions. Appl. Anal. Disc. Math. 1 (2007) 211-216
3. Arandelovic I.A. On a fixed point theorem of Kirk. J. Math. Anal. Appl. 301 (2005) 384-385
4. Aubin J.P., and Ekeland I. Applied Nonlinear Analysis (1984), John Wiley and Sons, Inc.
5. Aubin J.P., and Frankowska H. Set-Valued Analysis (1990), Birkhäuser, Boston
6. Aubin J.P., and Siegel J. Fixed points and stationary points of dissipative multivalued maps. Proc. Amer. Math. Soc. 78 (1980) 391-398
7. Banach S. Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales. Fundam. Math. 3 (1922) 133-181
8. Berge C. Topological Spaces (1963), Oliver & Boyd, Edinburgh
9. Briseid E.M. A rate of convergence for asymptotic contractions. J. Math. Anal. Appl. 330 (2007) 364-367
10. Briseid E.M. Some results on Kirk's asymptotic contractions. Fixed Point Theory 8 (2007) 17-27
11. Chen Y.-Z. Asymptotic fixed points for nonlinear contractions. Fixed Point Theory Appl. 2005 2 (2005) 213-217
12. Gerhardy P. A quantitative version of Kirk's fixed point theorem for asymptotic contractions. J. Math. Anal. Appl. 316 (2006) 339-345
13. Justman M. Iterative processes with "nucleolar" restrictions. Int. J. Game Theory 6 (1978) 189-212
14. Kirk W.A. Fixed points of asymptotic contractions. J. Math. Anal. Appl. 277 (2003) 645-650
15. Klein E., and Thompson A.C. Theory of Correspondences (1984), John Wiley & Sons, Inc., New York
16. Maschler M., and Peleg B. Stable sets and stable points of set-valued dynamic systems with applications to game theory. SIAM J. Control Optim. 14 (1976) 985-995
17. Meir A., and Keeler E. A theorem on contraction mappings. J. Math. Anal. Appl. 28 (1969) 326-329
18. Nussbaum R.D. Some asymptotic fixed point theorems. Trans. Amer. Math. Soc. 171 (1972) 349-375
19. Suzuki T. A definitive result on asymptotic contractions. J. Math. Anal. Appl. 335 (2007) 707-715
20. Suzuki T. Fixed-point theorem for asymptotic contractions of Meir-Keeler type in complete metric spaces. Nonlinear Anal. 64 (2006) 971-978
21. E. Tarafdar, R. Vyborny, A Generalized (Multivalued) Contraction Mapping Principle, in: Res. Rep. Pure Math., vol. 54, The University of Queensland, Australia, 1976
22. Tarafdar E., and Yuan G.X.-Z. Set-valued topological contractions. Appl. Math. Lett. 8 (1995) 79-81
23. Włodarczyk K., Klim D., and Plebaniak R. Existence and uniqueness of endpoints of closed set-valued asymptotic contractions in metric spaces. J. Math. Anal. Appl. 328 (2007) 46-57
24. Włodarczyk K., Obczyński C., and Wardowski D. Set-valued dynamic systems and random iterations of set-valued weaker contractions in uniform spaces. J. Math. Anal. Appl. 318 (2006) 772-780
25. Włodarczyk K., Plebaniak R., and Obczyński C. Endpoints of set-valued dynamical systems of asymptotic contractions of Meir-Keeler type and strict contractions in uniform spaces. Nonlinear Anal. 67 (2007) 1668-1679
26. Włodarczyk K., Plebaniak R., and Obczyński C. The uniqueness of endpoints for set-valued dynamical systems of contractions of Meir-Keeler type in uniform spaces. Nonlinear Anal. 67 (2007) 3373-3383
27. Włodarczyk K., and Plebaniak R. Endpoint theory for set-valued nonlinear asymptotic contractions with respect to generalized pseudodistances in uniform spaces. J. Math. Anal. Appl. 339 (2008) 344-358
28. Yuan G.X.-Z. KKM Theory and Applications in Nonlinear Analysis (1999), Marcel Dekker, New York