Abstract:
A vector space X is called an ordered vector space if for any elements x, y, z ∈ X and α ∈ R+,
x ⪯ y implies x + z ≤ y + z and 0 ≤ x implies 0 ≤ αx. If in addition, X is a lattice, that is if for
a pair {x, y} the inf{x, y} and sup{x, y} exists, then X is a Riesz space (or a vector lattice). In
this study, we discuss Banach lattices, ordered Banach spaces, operators on these spaces and their
applications in economics, fixed-point theory, differential and integral equations.
