‎Fixed point results for increasing mapping and the relationship between ‎(‎relative) algebraic interior and topological interior

In this ‎paper,‎ we show that the relative algebraic interior is a suitable replacement for both of the topological interior and the algebraic interior for the cases where these are empty‎. ‎Also‎, ‎we presente ‎some ‎properties ‎of ‎(‎relative)‎ algebraic ‎interior ‎and‎ ‎some fixed point theorems for increasing mapping‎. ‎The results obtained can be viewed as an extension and improvement of ‎the known corresponding results‎‎. ‎Some examples are provided here to support our conclusions‎.