(untitled) (Analysis in Theory and Applications, 2018)
In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Chebyshev. Examples of those algebras are given including the algebras of continuous functions on compact sets. We also see some results in C^*-algebras and Hilbert C^*-modules. Next, by considering some conditions, we study Chebyshev of subalgebras in C^*-algebras.