On Quasi-Pseudometric Type Spaces

Kazeem, Eniola Funmilayo; Agyingi, Collins Amburo; Gaba, Yaé Ulrich

doi:10.1155/2014/198685

Cited by 12 publications

(8 citation statements)

References 4 publications

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“…For some references on this structure, see [Kim68,Kün01,KAG14]. An immediate property is that if d is a quasi-pseudometric with the T0 condition then D(x, y) = max{d(x, y), d(y, x)} gives a metric.…”

Section: Hausdorff Distancementioning

confidence: 99%

Grassmann angles between real or complex subspaces

Mandolesi

2019

Preprint

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The Grassmann angle unifies and extends several concepts of angle between subspaces found in the literature, being defined for subspaces of equal or different dimensions, in a real or complex inner product space. It is related to Grassmann's exterior algebra and to the Fubini-Study and Hausdorff distances, and describes how Lebesgue measures contract under orthogonal projections. This angle is asymmetric for subspaces of different dimensions, turning the total Grassmannian of all subspaces into a quasipseudometric space. Other odd characteristics, already present in former angle concepts but usually overlooked, are explained, like its behavior with respect to orthogonal complements and realifications. We use it to study the Plücker embedding of Grassmannians, and to get an obstruction on complex structures for pairs of subspaces.

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Section: Hausdorff Distancementioning

confidence: 99%

Grassmann angles between real or complex subspaces

Mandolesi

2019

Preprint

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“…An interesting direction to look into is that of the quasi-pseudometric type spaces which were investigated by Kazeem et al [10]. In [10], we can read the following definition for a quasi-pseudometric type space:…”

Section: Common Fixed Point Theorems ( Kannan-choudhury Case)mentioning

confidence: 99%

Weak contractions via $λ$-sequences

Agyingi¹,

Gaba²

2018

Preprint

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“…Theorem 6.2 Let (X, D, α) be a complete metric type space with α ≥ 1, let T : X → X, and suppose there exists γ ∈ S such that for each x, y ∈ X, D(T x, T y) ≤ γ(D(x, y))D(x, y). (6) Then T has a unique fixed point z and for every x 0 ∈ X, the sequence {T n (x 0 )} converges to z.…”

Section: Extensions Of Banach's Principlementioning

confidence: 99%