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

Authors

  • Bhuwan Prasad Ojha Central Department of Mathematics, Tribhuvan University, Kirtipur, Nepal
  • Prakash Muni Bajrayacharya Central Department of Mathematics, Tribhuvan University, Kirtipur, Nepal

DOI:

https://doi.org/10.3126/mefc.v4i4.26360

Keywords:

Best approximation, Birkhoff orthogonality, Pythagorean orthogonality, Isosceles orthogonality, Ɛ – best approximation

Abstract

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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Published

2019-11-15

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Articles