# A generalization of Lim's lemma

Volume 14, Issue 1, pp 48--53
Publication Date: June 13, 2020 Submission Date: December 01, 2019 Revision Date: April 24, 2020 Accteptance Date: May 11, 2020
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### Authors

M. Ait Mansour - Département de Physique, LPFAS, Faculté Poly-disciplinaire, Safi, Université Cadi Ayyad, Morocco. M.A. Bahraoui - Département de Mathématiques, Faculté des Sciences et Techniques, Tanger, Université Abdelmalek Essaadi, Morocco. A. El Bekkali - Département de Mathématiques, Faculté des Sciences et Techniques, Tanger, Université Abdelmalek Essaadi, Morocco.

### Abstract

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.

### Share and Cite

##### ISRP Style

M. Ait Mansour, M.A. Bahraoui, A. El Bekkali, A generalization of Lim's lemma, Journal of Nonlinear Sciences and Applications, 14 (2021), no. 1, 48--53

##### AMA Style

Mansour M. Ait, Bahraoui M.A., El Bekkali A., A generalization of Lim's lemma. J. Nonlinear Sci. Appl. (2021); 14(1):48--53

##### Chicago/Turabian Style

Mansour, M. Ait, Bahraoui, M.A., El Bekkali, A.. "A generalization of Lim's lemma." Journal of Nonlinear Sciences and Applications, 14, no. 1 (2021): 48--53

### Keywords

• Fixed point
• Lim's lemma
• Nadler's fixed point theorem
• contraction mappings
• Hardy-Rogers mappings

•  47H10
•  54H25

### References

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