On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings

Abstract

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixed point, relaxation of the relatively compactness and the continuity on the map with replacing topological interior of the cone by the algebraic interior. Moreover, by applying Ascoli-Arzela's theorem an example in order to show that the main theorem of the paper [textit{An intermediate value theorem for monotone operators in ordered Banach spaces}, Fixed point theory and applications, 2012 (1) (2012) 1-4] may fail, is established.