The Moore-Penrose Inverse: A Fixed Point Method

Document Type : Original Article

Authors

1 Department of Basic Sciences, Birjand University of Technology, Birjand, Iran.

2 Department of Mathematics, Hakim Sabzevari University, Sabzevar, Iran.

Abstract

‎In this paper‎, ‎we establish several fixed-point theorems in the setting of orthogonal spaces (O-spaces)‎. ‎Our primary contribution is to extend the fixed-point theorem of Cabrera‎, ‎Harjani‎, ‎and Sadarangani $[\text{Ann‎. ‎Univ‎. ‎Ferrara}\ (2013)$ 59:251--258] to O-sets‎, ‎broadening its applicability‎. ‎Additionally‎, ‎we present novel results concerning the Moore--Penrose inverse‎, ‎exploring its properties and potential applications in functional analysis‎. ‎These findings contribute to both fixed-point theory and generalized inverses in partially structured spaces‎. ‎Also‎, ‎we show that the Moore--Penrose inverse of $A$‎, ‎denoted by $A^\dagger$‎, ‎can be computed as the fixed point of a contractive‎, ‎orthogonal‎, ‎and $\perp$-preserving mapping $T$‎.

Keywords

Main Subjects

References

[1] Baghani, H., Eshaghi Gordji, M., & Ramezani, M. (2016). Orthogonal sets: The axiom of choice and proof of a fixed point theorem. J. Fixed Point Theory Appl., 18, 465–477. DOI: https://doi.org/10.1007/s11784-016-0297-9.
[2] Baghani, H., Feckan, M., Farokhi-Ostad, J., & Alzabut, J. (2022). New existence and uniqueness result for fractional Bagley-Torvik differential equation. Miskolc Mathematical Notes, 23(2), 537–549. DOI: https://doi.org/10.18514/MMN.2022.3702.
[3] Baghani, H., Ramezani, M., & Khodaei, H. (2022). Orthogonal sets: Coincidence and fixed point theorems in incomplete metric spaces. Journal of New Researches in Mathematics, 6(27), 107–118.
[4] Cabrera, I., Harjani, J., & Sadarangani, K. (2013). A fixed point theorem for contractions of rational type in partially ordered metric spaces. Ann. Univ. Ferrara, 59, 251–258. DOI: https://doi.org/10.1007/s11565-013-0176-x.
[5] Eshaghi Gordji, M., & Habibi, H. (2017). Fixed point theory in generalized orthogonal metric space. Journal of Linear and Topological Algebra, 6(3), 251–260.
[6] Eshaghi Gordji, M., Ramezani, M., De la Sen, M., & Cho, Y.J. (2017). On orthogonal sets and Banach fixed point theorem. Fixed Point Theory, 18(2), 569–578. DOI: https://doi.org/10.24193/fpt-ro.2017.2.45.
[7] Jalaeian, M., Mohammadzadeh Karizaki, M., & Hassani, M. (2021). The product of operators and their Moore-Penrose inverses on Hilbert C∗-modules. Operators and Matrices, 15(1), 341–355. DOI: https://doi.org/10.7153/oam-2021-15-24.
[8] Kanwal, T., Hussain, A., Baghani, H., & De la Sen, M. (2020). New Fixed Point Theorems in Orthogonal F -Metric Spaces with Application to Fractional Differential Equation. Symmetry, 12(5), Article 832. DOI: https://doi.org/10.3390/sym12050832.
[9] Mohammadzadeh Karizaki, M., & Farokhi-Ostad, J. (2023). New Identities for Moore–Penrose Inverses of Some Operator Products and Their Reverse-order Laws. Acta Mathematica Sinica, English Series, 39, 2414–2426. DOI: https://doi.org/10.1007/s10114-023-1645-5.
Measure Algebras and Applications
Volume 3, Issue 2 - Serial Number 5
December 2025
Pages 61-69

Files

Share

How to cite

Statistics