Mathematics and Statistics Vol. 9(4), pp. 574 - 578
DOI: 10.13189/ms.2021.090416
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Quasi-Chebyshevity in

Jamila Jawdat ^*, Ayat Kamal
Mathematics Department, Zarqa University, Zarqa, Jordan

ABSTRACT

This paper deals with Quasi-Chebyshevity in the Bochner function spaces , where X is a Banach space. For W a nonempty closed subset of X and x ∊ X, an element w0 in W is called "best approximation" to x from W, if , for all w in W. All best approximation points of x from W form a set usually denoted by P_W (x). The set W is called "proximinal" in X if P_W (x) is non empty, for each x in X. Now, W is said to be "Quasi-Chebyshev" in X whenever, for each x in X, the set P_W (x) is nonempty and compact in X. This subject was studied in general Banach spaces by several authors and some results had been obtained. In this work, we study Quasi-Chebyshevity in the Bochner L^p- spaces. The main result in this paper is that: given W a Quasi-Chebyshev subspace in X then L^p(μ, W) is Quasi-Chebyshev in , if and only if L¹ (μ, W) is Quasi-Chebyshev in L¹(μ, X). As a consequence, one gets that if W is reflexive in X such that X satisfies the sequential KK-property then L^p(μ, W) is Quasi-Chebyshev in .

KEYWORDS
Quasi-Chebyshev Set, Proximinal Set, Compact Set, Reflexive Subspace, Sequential KK-property

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Jamila Jawdat , Ayat Kamal , "Quasi-Chebyshevity in ," Mathematics and Statistics, Vol. 9, No. 4, pp. 574 - 578, 2021. DOI: 10.13189/ms.2021.090416.

(b). APA Format:
Jamila Jawdat , Ayat Kamal (2021). Quasi-Chebyshevity in . Mathematics and Statistics, 9(4), 574 - 578. DOI: 10.13189/ms.2021.090416.