Title ON SIMULTANEOUS WEAKLY-CHEBYSHEV SUBSPACES Type of Research Article Keywords dual space, best simultaneous approximation, simultaneous quasi-Chebyshev subspace, simultaneous weakly-Chebyshev subspace Abstract In this paper, we shall introduce and characterize simultaneous quasi-Chebyshev (and weakly-Chebyshev) subspaces of normed spaces with respect to a bounded set S by using elements of the dual space. Researchers Shahram Rezapour (First Researcher)، Hosein Alizadeh (Second Researcher)، Seyyes Mansour Vaezpour (Third Researcher)