On an Inequality Related to the Isotonicity of the Projection Operator Original Research Article

In connection to the study of the isotonicity of the projection operator onto a closed convex set in an ordered Hilbert space, Isac has recently remarked the importance of an inequality named “the property of four elements” (PFE). In this paper a sharp inequality closely connected to (PFE) is proved in a Banach space setting. The property (PFE)Vfor Lyapunov functionalsVis introduced and studied. Some applications are included.