Weakly Picard mappings
Rus, Ioan A.
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 769-773 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1993-01-01
Classification:  47H10,  54H25
@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/

Barbuti U.; Guerra S. Osservazioni sopra una nota precedente, Rend. Ist. di Matem. Univ. Trieste 3 (1971), 1-12. (1971) | MR 0313892

Bellen A. Non-cyclic transformation and uniform convergence of the Picard sequences, Rend. Ist. di Matem. Univ. Trieste 4 (1972), 1-7. (1972) | MR 0336725

Bessaga C. On the converse of the Banach fixed point principle, Colloq. Math. 7 (1959), 41-43. (1959) | MR 0111015 | Zbl 0089.31501

Browder F.E.; Petryshyn W.V. The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Soc. 72 (1966), 571-575. (1966) | MR 0190745 | Zbl 0138.08202

Belluce L.P.; Kirk W.A. Some fixed point theorems in metric and Banach spaces, Canad. Math. Bull. 12 (1969), 481-491. (1969) | MR 0250148 | Zbl 0195.42901

Coroian L. $\alpha _{DP}$-condensing mappings, Univ. of Cluj-Napoca, Preprint No. 3, 1988, 17-22. | MR 0975265

Iseki K. Fixed point theorems in generalized complete metric space, Tamkang J. Math. 5 (1974), 213-219. (1974) | MR 0365542

Janoš L. A converse of the Banach's contraction theorem, Proc. Amer. Math. Soc. 18 (1967), 287-289. (1967) | MR 0208589

Janoš L.; Ko H.-M.; Tan K.-K. Edelstein's contractivity and attractors, Proc. Amer. Math. Soc. 76 (1979), 339-344. (1979) | MR 0537101 | Zbl 0411.54031

Leader S. Uniformly contractive fixed points in compact metric spaces, Proc. Amer. Math. Soc. 86 (1982), 153-158. (1982) | MR 0663887 | Zbl 0507.54040

Meyers P.R. A converse to Banach's contraction theorem, J. Res. Nat. Bureau of Standard 71B (1971), 73-76. (1971) | MR 0221469

Opoijcev W.I. The converse of the contraction mapping principle (in Russian), Usp. Mat. Nauk 31 (1976), 169-198. (1976) | MR 0420591

Rhoades B.E. Contractive definitions revisited, Contemporary Math. 21 (1983), 189-205. (1983) | MR 0729516 | Zbl 0528.54037

Rus I.A. Principii şi aplicaţii ale teoriei punctului fix, Ed. Dacia, Cluj-Napoca, 1979.

Rus I.A. Generalized contractions, Univ. Cluj-Napoca, Preprint No. 3, 1983, 1-30. | MR 0782679

Rus I.A. Bessaga mappings, Proc. Colloq. Approx. Optimization, Cluj-Napoca, 1984, 165-175. | MR 0847265 | Zbl 0572.54040

Rus I.A. Picard mappings: results and problems, Univ. Cluj-Napoca, Preprint No. 6, 1987, 55-64. | MR 0993513 | Zbl 0654.54030

Rus I.A. Picard mappings I., Studia Univ. Babeş-Bolyai 33 (1988), 70-73. (1988) | MR 1004822 | Zbl 0672.47049

Rus I.A. Basic problems of the metric fixed point theory revisited, Studia Univ. Babeş-Bolyai 34 (1989), 61-69. (1989) | MR 1073756 | Zbl 0878.54028

Rus I.A.; Mureşan A.S. Examples and counterexamples for Janoš mappings, Univ. Cluj-Napoca, Preprint No. 3, 1984, 63-66. | MR 0807962

Tan K.-K. Remark on contraction mappings, Boll. U.M.I. 9 (1974), 23-27. (1974) | MR 0358750 | Zbl 0295.54054

Volčič A. Some remarks on a S. Chu and R.D. Moyer's theorem, Rend. Accad. Naz. Lincei 49 (1970), 236-241. (1970) | MR 0295325