Fixed point theorems for new contractions with application in dynamic programming
DOI:
https://doi.org/10.21638/spbu01.2021.213Abstract
In this study, we give a generalization of the well-known Reich fixed point in the setting of general topological spaces with τ -distances. As applications of the obtained result, we prove some fixed point theorems for new contraction types in metric spaces. Moreover, we establish the existence and the uniqueness of solutions for a class of functional equations arising in dynamic programming.Keywords:
fixed point, strict contraction, generalized E-weakly contractive maps, metric spaces, Hausdorff topological spaces, dynamic programming
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References
Литература
1. Reich S. Kannans fixed point theorem. Boll. Unione Mat. Ital. 4 (4), 111 (1971).
2. Aamri M., El Moutawakil D. t-distance in general topological spaces with application to fixed point theory. Southwest Journal of Pure and Applied Mathematics, iss. 2 (2003).
3. Alber Y. I., Guerre-Delabriere S. Principle of Weakly Contractive Maps in Hilbert Spaces. In: Gohberg I., Lyubich Y. (eds.) Operator Theory: Advances and Applications. New Results in Operator Theory and Its Applications. Vol. 98. Basel, Birkh¨auser (1997). https://doi.org/10.1007/978-3-0348-8910-0_2
4. Edelstein M. On fixed and periodic points under contractive mappings. J. London Math. Soc. 37, 771–779 (1986).
5. Rhoades B.E. Some theorems on weakly contractive maps. Nonlinear Analysis 47, 2683–2693 (2001).
6. Bellman R. Dynamic Programming. Princeton, Princeton University Press (1957).
7. Bellman R., Lee E.S. Functional equations arising in dynamic programming. Aequ. Math. 17, 118 (1978).
References
1. Reich S. Kannans fixed point theorem. Boll. Unione Mat. Ital. 4 (4), 111 (1971).
2. Aamri M., El Moutawakil D. t-distance in general topological spaces with application to fixed point theory. Southwest Journal of Pure and Applied Mathematics, iss. 2 (2003).
3. Alber Y. I., Guerre-Delabriere S. Principle of Weakly Contractive Maps in Hilbert Spaces. In: Gohberg I., Lyubich Y. (eds.) Operator Theory: Advances and Applications. New Results in Operator Theory and Its Applications. Vol. 98. Basel, Birkh¨auser (1997). https://doi.org/10.1007/978-3-0348-8910-0_2
4. Edelstein M. On fixed and periodic points under contractive mappings. J. London Math. Soc. 37, 771–779 (1986).
5. Rhoades B.E. Some theorems on weakly contractive maps. Nonlinear Analysis 47, 2683–2693 (2001).
6. Bellman R. Dynamic Programming. Princeton, Princeton University Press (1957).
7. Bellman R., Lee E.S. Functional equations arising in dynamic programming. Aequ. Math. 17, 118 (1978).
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Published
2021-07-21
How to Cite
Touail, Y., & El Moutawakil, D. (2021). Fixed point theorems for new contractions with application in dynamic programming. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8(2), 338–348. https://doi.org/10.21638/spbu01.2021.213
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Section
Mathematics
License
Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
