A new common fixed point theorem on orthogonal metric spaces and an application

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Abstract

In the present work, a common fixed point result for self-mappings on orthogonal complete metric spaces, which are not necessarily complete, is proved. Furthermore, as an application, we find the existence of solutions to two differential equations.

About the authors

Youssef Touail

Université Sidi Mohamed Ben Abdellah

Email: youssef9touail@gmail.com
ORCID iD: 0000-0003-3593-8253
https://www.mathnet.ru/person186040

Département de Mathématique; FSDM, Faculté des Sciences Dhar El Mahraz

Morocco, Fez

Amine Jaid

Université Sultan Moulay Slimane

Email: aminejaid1990@gmail.com
ORCID iD: 0000-0001-7322-2008
https://www.mathnet.ru/person193681

Equipe de Recherche en Mathématiques Appliquées, Technologies de l’Information et de la Communication; Faculté Polydisciplinaire de Khouribga

Morocco, Beni-Mellal

Driss El Moutawakil

Université Chouaib Doukkali

Author for correspondence.
Email: d.elmotawakil@gmail.com
ORCID iD: 0000-0003-3082-0125
https://www.mathnet.ru/person193640

Département de Mathématique; Ecole Supérieure de l’Education et de la Formation

Morocco, El Jadida

References

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  2. Gordji M. E., Rameani M., De La Sen M., Cho Y.J. On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 2017, vol. 18, no. 2, pp. 569–578. DOI: https://doi.org/10.24193/fpt-ro.2017.2.45.
  3. Baghani H., Eshaghi Gordji M., Ramezani M. Orthogonal sets: The axiom of choice and proof of a fixed point theorem, J. Fixed Point Theory Appl., 2016, vol. 18, pp. 465–477. DOI: https://doi.org/10.1007/s11784-016-0297-9.
  4. Khalehoghli S., Rahimi H., Eshaghi Gordji M. Fixed point theorems in R-metric spaces with applications, AIMS Mathematics, 2020, vol. 5, no. 4, pp. 3125–3137. DOI: https://doi.org/10.3934/math.2020201.
  5. Touail Y., El Moutawakil D. Fixed point theorems on orthogonal complete metric spaces with an application, Int. J. Nonl. Anal. Appl., 2021, vol. 12, no. 2, pp. 1801–1809. DOI: https://doi.org/10.22075/ijnaa.2021.23033.2464.
  6. Jaid J., Touail Y., El Moutawakil D. On μF -contraction: New types of fixed points and common fixed points in Banach spaces, Asian-European J. Math., 2023, vol. 16, no. 11, 2350198. DOI: https://doi.org/10.1142/S179355712350198X.
  7. Touail Y., El Moutawakil D. ew 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.
  8. Touail Y., El Moutawakil D. Some new common fixed point theorems for contractive selfmappings with applications, Asian-European J. Math., 2022, vol. 15, no. 4, 2250080. DOI: https://doi.org/10.1142/S1793557122500802.
  9. Touail Y., Jaid A., El Moutawakil D. A note on common fixed point theorems in a bounded metric space, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2023, vol. 27, no. 2, pp. 241–249. EDN: ZXSBPZ. DOI: https://doi.org/10.14498/vsgtu1940.

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