International Journal of Nonlinear Analysis and Applications
Fixed point theorems on orthogonal complete metric spaces with an application
Document Type : Research Paper
Authors
Equipe de Recherche en Math'{e}matiques Appliqu'{e}es, Technologies de l'Information et de la Communication Facult'{e} Polydisciplinare de Khouribga, Universit'{e} Sultan Moulay Slimane de Beni-Mellal, Morocco
Abstract
In this paper, we introduce the concept of orthogonal contractive mappings and prove some fixed point theorems for such contractions. We establish our results in orthogonal bounded complete metric spaces via the notion of $\tau-$distances. Moreover, an application to a differential equation is given.
Keywords
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(2017) 251–260.
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Nonlinear Anal. Appl. 11(2) (2020) 425–436.
[7] S. Khalehoghli, H. Rahimi and M. Eshaghi, Fixed point theorems in R-metric spaces with applications, AIMS
Math. 5(4) (2020) 3125–3137.
[8] S. Khalehoghli, H. Rahimi and M. Eshaghi Gordji, R-topological spaces and SR-topological spaces with their
applications, Math. Sci. 14 (2020) 249-–255.
[9] M. Ramezani and H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear
Anal. Appl. 8(2) (2017) 23–28.
[10] B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001) 2683–2693.
[11] Y. Touail, D. El Moutawakil and S. Bennani, Fixed Point theorems for contractive selfmappings of a bounded
metric space, J. Funct. Spac. 2019 (2019) Article ID 4175807.
[12] Y. Touail and D. El Moutawakil, Fixed point results for new type of multivalued mappings in bounded metric
spaces with an application, Ricerche mat (2020).
[13] Y. Touail and D. El Moutawakil, New common fixed point theorems for contractive self mappings and an application to nonlinear differential equations, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 903–911.
[14] Y. Touail and D. El Moutawakil, Fixed point theorems for new contractions with application in dynamic programming, Vestnik St. Petersb. Univ. Math. 54 (2021) 206-–212.
[15] Y. Touail and D. El Moutawakil, Some new common fixed point theorems for contractive selfmappings with
applications Asian-European J. Math. (2021) https://doi.org/10.1142/S1793557122500802.
Southwest J. Pure Appl. Math. 2003(2) (2003) 1–5.
[2] Ya. I. Alber and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, new results in
operator theory, Adv. Appl. (ed. by I. Gohberg and Yu Lyubich), Birkhauser verlag, Basel 98 (1997) 7—22.
[3] Z. Eivazi Damirchi Darsi Olia, M. Eshaghi Gordji and D. Ebrahimi Bagha, Banach fixed point theorem on
orthogonal cone metric spaces, Fact Univ. 35(5) (2020) 1239–1250.
[4] M. Eshaghi Gordji, M. Ramezani, M. De La Sen and Y.J. Cho, On orthogonal sets and Banach fixed point
theorem, Fixed Point Theory 18 (2017) 569—578.
[5] M.E. Gordji and H. Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Top. Alg. 6(3)
(2017) 251–260.
[6] H. Hosseini and M. Eshaghi Gordji, (2020), Fixed point results in orthogonal modular metric spaces, Int. J.
Nonlinear Anal. Appl. 11(2) (2020) 425–436.
[7] S. Khalehoghli, H. Rahimi and M. Eshaghi, Fixed point theorems in R-metric spaces with applications, AIMS
Math. 5(4) (2020) 3125–3137.
[8] S. Khalehoghli, H. Rahimi and M. Eshaghi Gordji, R-topological spaces and SR-topological spaces with their
applications, Math. Sci. 14 (2020) 249-–255.
[9] M. Ramezani and H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear
Anal. Appl. 8(2) (2017) 23–28.
[10] B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001) 2683–2693.
[11] Y. Touail, D. El Moutawakil and S. Bennani, Fixed Point theorems for contractive selfmappings of a bounded
metric space, J. Funct. Spac. 2019 (2019) Article ID 4175807.
[12] Y. Touail and D. El Moutawakil, Fixed point results for new type of multivalued mappings in bounded metric
spaces with an application, Ricerche mat (2020).
[13] Y. Touail and D. El Moutawakil, New common fixed point theorems for contractive self mappings and an application to nonlinear differential equations, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 903–911.
[14] Y. Touail and D. El Moutawakil, Fixed point theorems for new contractions with application in dynamic programming, Vestnik St. Petersb. Univ. Math. 54 (2021) 206-–212.
[15] Y. Touail and D. El Moutawakil, Some new common fixed point theorems for contractive selfmappings with
applications Asian-European J. Math. (2021) https://doi.org/10.1142/S1793557122500802.
)
Volume 12, Issue 2
November 2021Pages 1801-1809
- Receive Date: 02 March 2021
- Revise Date: 11 April 2021
- Accept Date: 28 April 2021