Shahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-795210120210501RELATIONS BETWEEN TWO CLASSES OF FUNCTIONS103110289810.22103/jmmrc.2021.14614.1100ENJavadFathi MourjaniDepartment of Mathematics, University of hormozgan, Bandarabbas, IranJournal Article20190825Let F denote a specific space of the class of was costructed by H. Khodabakhshian<br /> as a classes of separable Banach function spaces analogous to the james function spaces. In this<br /> notes we prove that l_p(α) is isomorphic to a complemented subspace of F_{α,p} and for p = 2, F_{α,p} is a closed subspace of the Waterman-Shiba space αBV^ (p)<br /> Assume F denotes a specific space of the class of F_{α,p} that was costructed by H.<br /> Khodabakhshian[2] as a classes of separable Banach function spaces analogous to the James<br /> function spaces. In this notes we prove that l_p(α) is isomorphic to a complemented subspace of<br /> F_{α,p} and for p = 2, F_{α,p} is a closed subspace of Waterman-Shiba space αBV^(p).https://jmmrc.uk.ac.ir/article_2898_15b1dc06ab3b9894b5907d89048d7188.pdf