Let X be a convex metric space, K a non-empty closed subset of X and T: K \rightarrow X 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 T has the so called property (M) and satisfies Rothe’s boundary condition, i.e., maps \partial K (the boundary of K) into K, then T has a fixed point in K. In this paper we observe that property \left( M\right) can be removed and, hence, the above fixed point theorem takes place in a different setting.

Additional Information


Alghamdi, Maryam A., Berinde, Vasile, Shahzad, Nasser