In this paper we generalize the well known converse to the contraction principle due to C. Bessaga, dropping the uniqueness of the fixed point from its hypotheses. Some properties of weakly Picard mappings are given.
@article{118632, author = {Ioan A. Rus}, title = {Weakly Picard mappings}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {769-773}, zbl = {0787.54045}, mrnumber = {1263804}, language = {en}, url = {http://dml.mathdoc.fr/item/118632} }
Rus, Ioan A. Weakly Picard mappings. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 769-773. http://gdmltest.u-ga.fr/item/118632/
Osservazioni sopra una nota precedente, Rend. Ist. di Matem. Univ. Trieste 3 (1971), 1-12. (1971) | MR 0313892
Non-cyclic transformation and uniform convergence of the Picard sequences, Rend. Ist. di Matem. Univ. Trieste 4 (1972), 1-7. (1972) | MR 0336725
On the converse of the Banach fixed point principle, Colloq. Math. 7 (1959), 41-43. (1959) | MR 0111015 | Zbl 0089.31501
The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Soc. 72 (1966), 571-575. (1966) | MR 0190745 | Zbl 0138.08202
Some fixed point theorems in metric and Banach spaces, Canad. Math. Bull. 12 (1969), 481-491. (1969) | MR 0250148 | Zbl 0195.42901
$\alpha _{DP}$-condensing mappings, Univ. of Cluj-Napoca, Preprint No. 3, 1988, 17-22. | MR 0975265
Fixed point theorems in generalized complete metric space, Tamkang J. Math. 5 (1974), 213-219. (1974) | MR 0365542
A converse of the Banach's contraction theorem, Proc. Amer. Math. Soc. 18 (1967), 287-289. (1967) | MR 0208589
Edelstein's contractivity and attractors, Proc. Amer. Math. Soc. 76 (1979), 339-344. (1979) | MR 0537101 | Zbl 0411.54031
Uniformly contractive fixed points in compact metric spaces, Proc. Amer. Math. Soc. 86 (1982), 153-158. (1982) | MR 0663887 | Zbl 0507.54040
A converse to Banach's contraction theorem, J. Res. Nat. Bureau of Standard 71B (1971), 73-76. (1971) | MR 0221469
The converse of the contraction mapping principle (in Russian), Usp. Mat. Nauk 31 (1976), 169-198. (1976) | MR 0420591
Contractive definitions revisited, Contemporary Math. 21 (1983), 189-205. (1983) | MR 0729516 | Zbl 0528.54037
Principii şi aplicaţii ale teoriei punctului fix, Ed. Dacia, Cluj-Napoca, 1979.
Generalized contractions, Univ. Cluj-Napoca, Preprint No. 3, 1983, 1-30. | MR 0782679
Bessaga mappings, Proc. Colloq. Approx. Optimization, Cluj-Napoca, 1984, 165-175. | MR 0847265 | Zbl 0572.54040
Picard mappings: results and problems, Univ. Cluj-Napoca, Preprint No. 6, 1987, 55-64. | MR 0993513 | Zbl 0654.54030
Picard mappings I., Studia Univ. Babeş-Bolyai 33 (1988), 70-73. (1988) | MR 1004822 | Zbl 0672.47049
Basic problems of the metric fixed point theory revisited, Studia Univ. Babeş-Bolyai 34 (1989), 61-69. (1989) | MR 1073756 | Zbl 0878.54028
Examples and counterexamples for Janoš mappings, Univ. Cluj-Napoca, Preprint No. 3, 1984, 63-66. | MR 0807962
Remark on contraction mappings, Boll. U.M.I. 9 (1974), 23-27. (1974) | MR 0358750 | Zbl 0295.54054
Some remarks on a S. Chu and R.D. Moyer's theorem, Rend. Accad. Naz. Lincei 49 (1970), 236-241. (1970) | MR 0295325