Fixed points of non-self almost contractions

Let be a convex metric space, a non-empty closed subset of and a non-self almost contraction. Berinde and Păcurar [Berinde, V. and Păcurar, M., Fixed point theorems for nonself single-valued almost contractions, Fixed Point Theory, 14  (2013), No. 2, 301–312], proved that if has the so called property and satisfies Rothe’s boundary condition, i.e., maps (the boundary of ) into , then has a fixed point in . In this paper we observe that property can be removed and, hence, the above fixed point theorem takes place in a different setting.