An intermediate value theorem for monotone operators in ordered Banach spaces
Vadim V. Kostrykin, Anna Oleynik · Fixed Point Theory and Applications · 2012
We consider a monotone increasing operator in an ordered Banach space having and as a strong super- and subsolution, respectively. In contrast with the well-studied case , we suppose that . Under the assumption that the order cone is normal and minihedral, we prove the existence of a fixed point located in the order interval . MSC:47H05, 47H10, 46B40.