Fixed points for non-self operators and domain invariance theorems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 70, Issue 1, 2009, Pages 117-125

  Lazǎr, Tania A ^a   Petruşel, Adrian ^b   Shahzad, Naseer ^c  

^a Academy of Economic Studies   (Romania)

^b BABE BOLYAI UNIVERSITY   (Romania)

^c KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

Author keywords

Associated field; Data dependence; Domain invariance; Fixed point; Generalized contraction; Multivalued operator; Open operator

Indexed keywords

MATHEMATICAL TECHNIQUES; NONLINEAR ANALYSIS;

ASSOCIATED FIELD; DATA DEPENDENCE; FIXED POINTS; MULTIVALUED OPERATOR; OPEN OPERATOR;

FIXED POINT ARITHMETIC;

EID: 55749111402     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.11.037     Document Type: Article

References (32)

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. Agarwal R.P., Dshalalow J.H., and O'Regan D. Fixed point and homotopy results for generalized contractive maps of Reich type. Appl. Anal. 82 (2003) 329-350
3. J. Andres, L. Górniewicz, On the Banach contraction principle for multivalued mappings, Approximation, Optimization and Mathematical Economics (Pointe-à-Pitre, 1999), 1-23 Physica, Heidelberg, 2001
4. Aamri M., and Chaira K. Approximation du point fixe et applications faiblement contractantes. Extracta Math. 17 (2002) 97-110
5. Aubin J.P., and Frankowska H. Set-Valued Analysis (1990), Birkhauser, Basel
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. Bollenbacher A., and Hicks T.L. A fixed point theorem revisited. Proc. Amer. Math. Soc. 102 (1988) 898-900
8. Caristi J. Fixed points theorems for mappings satisfying inwardness conditions. Trans. Amer. Math. Soc. 215 (1976) 241-251
9. Covitz H., and Nadler Jr. S.B. Multivalued contraction mappings in generalized metric spaces. Israel J. Math. 8 (1970) 5-11
10. Dugundji J., and Granas A. Fixed Point Theory (2003), Springer Verlag, Berlin
11. Dugundji J., and Granas A. Weakly contractive maps and elementary domain invariance theorem. Bull. Greek Math. Soc. 19 (1978) 141-151
12. Frigon M., and Granas A. Résultats du type de Leray-Schauder pour les contractions multivoques. Topol. Methods Nonlinear Anal. 4 (1994) 197-208
13. Hegedüs M. New generalizations of Banach's contraction principle. Acta Sci. Math. (Szeged) 42 (1980) 87-89
14. Hegedüs M., and Szilágyi T. Equivalent conditions and a new fixed point theorem in the theory of contractive type mappings. Math. Japon. 25 (1980) 147-157
15. Hicks T.L., and Rhoades B.E. A Banach type fixed point theorem. Math. Japon. 24 (1979) 327-330
16. Jachymski J., and Jóźwik I. Nonlinear contractive conditions: A comparison and related problems. Banach Center Publ. 77 (2007) 123-146
17. Maciejewski M. Inward contractions on metric spaces. J. Math. Anal. Appl. 330 (2007) 1207-1219
18. Matkowski J. Integrable solutions of functional equations. Dissertationes Math. (Rozprawy Mat.) 127 (1975) 68
19. Meir A., and Keeler E. A theorem on contraction mappings. J. Math. Anal. Appl. 28 (1969) 326-329
20. Park S., and Kim W.K. Extensions of the weak contractions of Dugundji and Granas. J. Korean Math. Soc. 21 (1984) 1-7
21. Petruşel A. On Frigon-Granas-type multifunctions. Nonlinear Anal. Forum 7 (2002) 113-121
22. Petruşel A. Operatorial Inclusions (2002), House of the Book of Science, Cluj-Napoca
23. Petruşel A. Generalized multivalued contractions. Nonlinear Anal. 47 (2001) 649-659
24. Petruşel A., and Sîntǎmǎrian A. Single-valued and multi-valued Caristi type operators. Publ. Math. Debrecen 60 (2002) 167-177
25. Reich S. Fixed point of contractive functions. Boll. Unione Mat. Ital. 5 (1972) 26-42
26. Rus I.A. Fixed point theorems for multivalued mappings in complete metric spaces. Math. Japon. 20 (1975) 21-24
27. Rus I.A. Generalized Contractions and Applications (2001), Cluj University Press, Cluj-Napoca
28. Rus I.A. Basic problems of the metric fixed point theory revisited (II). Studia Univ. Babeş-Bolyai Math. 36 (1991) 81-89
29. Rus I.A., and Mureşan S. Data dependence of the fixed point set of weakly Picard operators. Studia Univ. Babeş-Bolyai Math. 43 (1998) 79-83
30. Rus I.A., Petruşel A., and Şerban M.A. Weakly Picard operators: equivalent definitions, applications and open problems. Fixed Point Theory 7 (2006) 3-22
31. Walter W. Remarks on a paper by F. Browder about contraction. Nonlinear Anal. 5 (1981) 21-25
32. Wȩgrzyk R. Fixed point theorems for multifunctions and their applications to functional equations. Dissertationes Math. (Rozprawy Mat.) 201 (1982) 28