### Journals Information

**
Mathematics and Statistics Vol. 9(4), pp. 574 - 578 DOI: 10.13189/ms.2021.090416 Reprint (PDF) (1164Kb) **

## 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 L^{1} (μ, W) is Quasi-Chebyshev in L^{1}(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.