This paper is connected with the theory of a-nonexpansive mappings, which were introduced by K. Goebel and M. A. J. Pineda in 2007. These mappings are a natural generalisation of nonexpansive mappings from the point of view of the fixed point theory. In particular, they proved that in Banach spaces all α = (α₁,..., α_n) -nonexpansive mappings with α₁ big enough, namely α₁≥2 (1/1-n), have minimal displacement equal to zero. This paper introduces some new results connected with this problem.

This paper is connected with the theory of a-nonexpansive mappings, which were introduced by K. Goebel and M. A. J. Pineda in 2007. These mappings are a natural generalisation of nonexpansive mappings from the point of view of the fixed point theory. In particular, they proved that in Banach spaces all α = (α₁,..., α_n) -nonexpansive mappings with α₁ big enough, namely α₁≥2 (1/1-n), have minimal displacement equal to zero. This paper introduces some new results connected with this problem.