Stability and hyperstability of orthogonally $$*$$ ∗ -m-homomorphisms in orthogonally Lie $$C^*$$ C ∗ -algebras: a fixed point approach

Bahraini, Ali; Askari, G.; Gordji, M. Eshaghi; Mafigholami, Roya

doi:10.1007/s11784-018-0571-0

Cited by 6 publications

(7 citation statements)

References 22 publications

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“…Then f has a unique fixed point x * ∈ X and lim n→∞ f n x = x * for all x ∈ X. [4] PROOF. Consider the metric subspace Y as in Theorem 2.1.…”

Section: Thenmentioning

confidence: 97%

Notes on Orthogonal-Complete Metric Spaces

Dung

2021

Bull. Aust. Math. Soc.

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We prove that the restriction of a given orthogonal-complete metric space to the closure of the orbit induced by the origin point with respect to an orthogonal-preserving and orthogonal-continuous map is a complete metric space. Then we show that many existence results on fixed points in orthogonal-complete metric spaces can be proved by using the corresponding existence results in complete metric spaces.

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“…Then f has a unique fixed point x * ∈ X and lim n→∞ f n x = x * for all x ∈ X. [4] PROOF. Consider the metric subspace Y as in Theorem 2.1.…”

Section: Thenmentioning

confidence: 97%

Notes on Orthogonal-Complete Metric Spaces

Dung

2021

Bull. Aust. Math. Soc.

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“…They also, proved the following theorem which can be considered as a real extension of Banach fixed point theorem [11,1,3,4,5,6,10].…”

Section: A Mappingmentioning

confidence: 98%

“…Eshaghi and et.al. [3] introduced the notion of orthogonal sets as follows (also see [11,1,4,5,6,10]): Definition 1.6. [3] Let X = φ and ⊥ ⊆ X × X be a binary relation.…”

Section: Introductionmentioning

confidence: 99%

Banach Fixed Point Theorem on Orthogonal Cone Metric Spaces

2021

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“…Recently, Eshaghi Gordji et al [21] introduced the notion of the orthogonal set which contains the notion of the orthogonality in normed space. By using the concept of orthogonal sets, Bahraini et al [22] proved the generalization of the Diaz-Margolis [23] fixed point theorem on these sets. e study on orthogonal sets has been done by several authors (for example, see [24][25][26]).…”

Section: Introductionmentioning

confidence: 99%