Some New Fixed Point Theorems for Contractive and Nonexpansive Mappings

Rajendra Pant

In the present paper, we obtain some new fixed point theorems for set-valued contractive and nonexpansive mappings in the setting of ultrametric spaces. Our theorems complement, generalize and extend some well known results of Petalas and Vidalis [A fixed point theorem in non-Archimedean vector spaces, Proc. Amer. Math. Soc 118 (1993), 819--821.], Suzuki [A new type of fixed point theorem in metric spaces, Nonlinear Anal. 71 (2009), 5313--5317.] and others.