1
Department of Basic sciences, Birjand university of Technology, Birjand, Iran.
2
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
10.22091/maa.2026.15531.1055
Abstract
In this paper, we establish several fixed-point theorems in the setting of orthogonal spaces (O-spaces). Our primary contribution is an extension of 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 $T$.
Farokhi Ostad, J., & Baghani, H. (2026). The Moore-Penrose Inverse: A Fixed Point Method. Measure Algebras and Applications, (), -. doi: 10.22091/maa.2026.15531.1055
MLA
Javad Farokhi Ostad; Hamid Baghani. "The Moore-Penrose Inverse: A Fixed Point Method". Measure Algebras and Applications, , , 2026, -. doi: 10.22091/maa.2026.15531.1055
HARVARD
Farokhi Ostad, J., Baghani, H. (2026). 'The Moore-Penrose Inverse: A Fixed Point Method', Measure Algebras and Applications, (), pp. -. doi: 10.22091/maa.2026.15531.1055
VANCOUVER
Farokhi Ostad, J., Baghani, H. The Moore-Penrose Inverse: A Fixed Point Method. Measure Algebras and Applications, 2026; (): -. doi: 10.22091/maa.2026.15531.1055
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