Email this article A note on common fixed point theorems in a bounded metric space
- Authors: Touail Y.1, Jaid A.1, El Moutawakil D.1
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Affiliations:
- Université Sultan Moulay Slimane
- Issue: Vol 27, No 2 (2023)
- Pages: 241-249
- Section: Differential Equations and Mathematical Physics
- URL: https://ogarev-online.ru/1991-8615/article/view/145900
- DOI: https://doi.org/10.14498/vsgtu1940
- ID: 145900
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Abstract
In this paper, we introduce the concept of Tβ-contraction for a pair of commuting self-mappings and prove a common fixed point theorem for this type. Our results improve and extend many existing results in the literature. The paper also contains an application for non-linear integral equations.
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About the authors
Youssef Touail
Université Sultan Moulay Slimane
Author for correspondence.
Email: youssef9touail@gmail.com
ORCID iD: 0000-0003-3593-8253
MATIC, Faculte Polydisciplinaire de Khouribga
Morocco, 23000, Beni-MellalAmine Jaid
Université Sultan Moulay Slimane
Email: aminejaid1990@gmail.com
ORCID iD: 0000-0001-7322-2008
MATIC, Faculte Polydisciplinaire de Khouribga
Morocco, 23000, Beni-MellalDriss El Moutawakil
Université Sultan Moulay Slimane
Email: d.elmotawakil@gmail.com
ORCID iD: 0000-0003-3082-0125
MATIC, Faculte Polydisciplinaire de Khouribga
Morocco, 23000, Beni-MellalReferences
- Jungck G., Rhoades B. E. Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 1998, vol. 29, no. 3, pp. 227–238.
- Samet B., Vetro C., Vetro P. Fixed point theorems for $alpha$-$psi$-contractive type mappings, Nonl. Anal., Th. Meth. Appl., 2012, vol. 75, no. 4, pp. 2154–2165. DOI: https://doi.org/10.1016/j.na.2011.10.014.
- Abdeljawad T. Meir-Keeler $alpha$-contractive fixed and common fixed point theorems, Fixed Point Theory Appl., 2013, vol. 2013, no. 1, 19. DOI: https://doi.org/10.1186/1687-1812-2013-19.
- Touail Y., El Moutawakil D. New common fixed point theorems for contractive self mappings and an application to nonlinear differential equations, Int. J. Nonlinear Anal. Appl., 2021, vol. 12, no. 1, pp. 903–911. DOI: https://doi.org/10.22075/IJNAA.2021.21318.2245.
- Touail Y., El Moutawakil D., Bennani S. Fixed point theorems for contractive selfmappings of a bounded metric space, J. Funct. Spaces, 2019, vol. 2019, 4175807. DOI: https://doi.org/10.1155/2019/4175807.
- Touail Y., El Moutawakil D. Fixed point results for new type of multivalued mappings in bounded metric spaces with an application, Ric. Mat., 2022, vol. 71, no. 2, pp. 315–323. DOI: https://doi.org/10.1007/s11587-020-00498-5.
- Touail Y., El Moutawakil D. $bot_{psi F}$-contractions and some fixed point results on generalized orthogonal sets, Rend. Circ. Mat. Palermo (2), 2021, vol. 70, no. 3, pp. 1459–1472. DOI: https://doi.org/10.1007/s12215-020-00569-4.
- Touail Y., El Moutawakil D. Fixed point theorems for new contractions with application in dynamic programming, Vestn. St. Petersbg. Univ., Math., 2021, vol. 54, no. 2, pp. 206–212. EDN: ZJHFQW. DOI: https://doi.org/10.1134/S1063454121020126.
- Touail Y., El Moutawakil D. Fixed point theorems on orthogonal complete metric spaces with an application, Int. J. Nonlinear Anal. Appl., 2021, vol. 12, no. 2, pp. 1801–1809. DOI: https://doi.org/10.22075/IJNAA.2021.23033.2464.
- Touail Y., El Moutawakil D. Some new common fixed point theorems for contractive selfmappings with applications, Asian-Eur. J. Math., 2022, vol. 15, no. 4, 2250080. DOI: https://doi.org/10.1142/S1793557122500802.
- Touail Y., Jaid A., El Moutawakil D. New contribution in fixed point theory via an auxiliary unction with an application, Ric. Mat., 2023, vol. 72, no. 1, pp. 181–191. DOI: https://doi.org/10.1007/s11587-021-00645-6.
- Aamri M., El Moutawakil D. $tau$-distance in general topological spaces $(X,tau)$ with application to fixed point theory, Southwest J. Pure Appl. Math., 2003, no. 2, pp. 1–6. https://eudml.org/doc/123956.
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