Geodesic
A generalization of Lim's lemma
Mansour, M. Ait 1 ; Bahraoui, M.A. 2 ; El Bekkali, A. 2
1 Département de Physique, LPFAS, Faculté Poly-disciplinaire, Safi, Université Cadi Ayyad, Morocco
2 Département de Mathématiques, Faculté des Sciences et Techniques, Tanger, Université Abdelmalek Essaadi, Morocco
Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 1, p. 48-53.

Voir la notice de l'article provenant de la source International Scientific Research Publications

It follows from [A. L. Dontchev, R. T. Rockafellar, Springer, New York, (2014), Theorem 5I.3] that the distance from a point $x$ to the set of fixed points of a set-valued contraction mapping $\Phi$ is bounded by a constant times the distance from $x$ to $\Phi$. In this paper, we generalize both this result and Lim's lemma for a larger class of set-valued mappings instead of the class of set-valued contraction mappings. As consequence, we obtain some known fixed points theorems.
DOI : 10.22436/jnsa.014.01.06
Classification : 47H10, 54H25
Keywords: Fixed point, Lim's lemma, Nadler's fixed point theorem, contraction mappings, Hardy-Rogers mappings

Mansour, M. Ait  1 ; Bahraoui, M.A.  2 ; El Bekkali, A.  2

1 Département de Physique, LPFAS, Faculté Poly-disciplinaire, Safi, Université Cadi Ayyad, Morocco
2 Département de Mathématiques, Faculté des Sciences et Techniques, Tanger, Université Abdelmalek Essaadi, Morocco 
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Mansour, M. Ait ; Bahraoui, M.A. ; El Bekkali, A. . A generalization of Lim's lemma. Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 1, p. 48-53. doi : 10.22436/jnsa.014.01.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.014.01.06/

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