Proximinality and co-proximinality in metric linear spaces

Narang, T. W.; Gupta, Sahil

doi:10.17951/a.2015.69.1.83

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Extension Theorem For Lh(xy)1

Introduction1

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Cited by 2 publications

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“…We first recall some important definitions and results. We mainly refer to [11]; see also [12][13][14][15][16][17]. Definition 3.1.…”

Section: Extension Theorem For Lh(xy)mentioning

confidence: 99%

On a new space consisting of norm maintaining functions

Norman

2019

Preprint

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In this paper we define a new space, LH(X, Y ), consisting of functions f ∈ X ⊂ Y (with X, Y normed spaces) such that f X ≡ f Y (where • X is any norm on X, in general not the norm induced by • Y on X). In Section 2 we study some properties involving LH and Schur's property, norm attainment and LHW (a weaker version of LH). In particular, one of the main results of this section states that strong and weak norm attainments together with some conditions imply that the considered function belongs to LHW or LH (depending on which conditions are satisfied). In Section 3 we renorm in a natural way the space Y so that LH(X, Y ) = X, obtaining an important extension Theorem.

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“…We first recall some important definitions and results. We mainly refer to [11]; see also [12][13][14][15][16][17]. Definition 3.1.…”

Section: Extension Theorem For Lh(xy)mentioning

confidence: 99%

On a new space consisting of norm maintaining functions

Norman

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Estimates in approximation theory that (cf [ 1] , [2], [3], [4]and [5] )has recently introduced [6] and [7] As in the case of best approximation, the theory of best co-approximation has been developed to a from obvious in metric space and Banach Characterization, Characterization of co-a proximal space by [8 ], [9] and [10].…”

Section: Introductionmentioning

confidence: 99%