Quasi-orthogonality of the best approximant sets

Mazaheri, H.; Ghaini, F. M. Maalek

doi:10.1016/j.na.2005.09.026

Cited by 11 publications

(5 citation statements)

References 2 publications

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“…Let X be a normed linear space and M be a subspace of X. Then 0 ∈ (x) if and only if x-0 ⊥ M (Mazaheri & Maalek, 2006). Proof.…”

Section: Introductionmentioning

confidence: 99%

Relation of Pythagorean and Isosceles Orthogonality with Best approximations in Normed Linear Space

Ojha¹,

Bajrayacharya²

2019

Math. Educ. Forum Nep.

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In an arbitrary normed space, though the norm not necessarily coming from the inner product space, the notion of orthogonality may be introduced in various ways as suggested by the mathematicians like R.C. James, B.D. Roberts, G. Birkhoff and S.O. Carlsson. We aim to explore the application of orthogonality in normed linear spaces in the best approximation. Hence it has already been proved that Birkhoff orthogonality implies best approximation and best approximation implies Birkhoff orthogonality. Additionally, it has been proved that in the case of ε -orthogonality, ε -best approximation implies ε -orthogonality and vice-versa. In this article we established relation between Pythagorean orthogonality and best approximation as well as isosceles orthogonality and ε -best approximation in normed space.

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“…Let X be a normed linear space and M be a subspace of X. Then 0 ∈ (x) if and only if x-0 ⊥ M (Mazaheri & Maalek, 2006). Proof.…”

Section: Introductionmentioning

confidence: 99%

Relation of Pythagorean and Isosceles Orthogonality with Best approximations in Normed Linear Space

Ojha¹,

Bajrayacharya²

2019

Math. Educ. Forum Nep.

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“…A proximinal subspace G is called quasi-Chebyshev if and only if P G (x) is compact, for all x ∈ X (see [3][4]). …”

Section: Introductionmentioning

confidence: 99%

The maps preserving approximation

Mazaheri

Zadeh²

2007

imf

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“…al [8][9][10][11][12]. Also there are some results on coapproximation in [2][3][4][5]. In this context, we shall obtain some results on orthogonality and coproximinality subspaces of normed space, and obtain properties on normed spaces that are similar to orthogonality in Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%