A common fixed point theorem for compatible mappings on a normed vector space.
A common fixed theorem is proved for two pairs of compatible mappings on a normed vector space.
In the setting of a b-metric space (see [Czerwik, S.: Contraction mappings in b-metric spaces Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11.] and [Czerwik, S.: Nonlinear set-valued contraction mappings in b-metric spaces Atti Sem. Mat. Fis. Univ. Modena 46, 2 (1998), 263–276.]), we establish two general common fixed point theorems for two mappings satisfying the (E.A) condition (see [Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions Math....
In this note a commutant lifting theorem for vector-valued functional Hilbert spaces over generalized analytic polyhedra in ℂⁿ is proved. Let T be the compression of the multiplication tuple to a *-invariant closed subspace of the underlying functional Hilbert space. Our main result characterizes those operators in the commutant of T which possess a lifting to a multiplier with Schur class symbol. As an application we obtain interpolation results of Nevanlinna-Pick and Carathéodory-Fejér type...