@article {
author = {Tourani, Rasul and Khoddami, Ali Reza},
title = {On E-Proximinality and Strongly Proximinality in Complex-Valued, Bounded and Continuous Functions Space},
journal = {Sahand Communications in Mathematical Analysis},
volume = {20},
number = {1},
pages = {119-136},
year = {2023},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2022.555067.1124},
abstract = {For a non-zero normed linear space $A$, we consider $ C^b\left(K\right) $, the complex-valued, bounded and continuous functions space on $K$ with $ \left\| \cdot \right\|_\infty $, where $ K = \overline{B^{\left(0\right)}_1} $ (the closed unit ball of $A$). Also for a non-zero element $\varphi \in A^*$ with $ \left\| \varphi \right\| \leq 1 $, we consider the space $ C^{b\varphi}\left(K\right) $ as the linear space $ C^b\left(K\right) $ with the new norm $ \left\| f \right\|_\varphi = \left\| f\varphi \right\|_\infty $ for all $ f \in C^b\left(K\right) $. Some basic properties such as, proximinality, E-proximinality, strongly proximinality and quasi Chebyshev for certain subsets of $ C^b\left(K\right) $ are characterized with the norms $ \left\| \cdot \right\|_\varphi $ and $ \left\|\cdot \right\|_\infty $. Some examples for illustration and for comparison between the norms $ \left\| \cdot \right\|_\varphi $ and $ \left\| \cdot \right\|_\infty $ on $ C^b\left(K\right) $ are presented.},
keywords = {Best approximation,E-proximinal,Quasi Chebyshev,Strongly proximinal},
url = {https://scma.maragheh.ac.ir/article_697999.html},
eprint = {https://scma.maragheh.ac.ir/article_697999_ae3c9744a2116ead476a7a52204b4ca7.pdf}
}