FIBER PICARD OPERATORS THEOREM AND APPLICATIONS

Abstract

In this paper we study the following problem: Let (X_k,d_k), k=0,p, p³1, be metric spaces and A_k:X₀´...´X_k®X_k, k=0,p be operators. We suppose that: (a) the operators A_k are continuous, k=0,p; (b) the operators A₀,A_k(x₀,...,x_k-1,×), k=1,p are (weakly) Picard operators. Establish conditions which imply that the operator B_p:X₀´...´X_p®X₀´...´X_p, B_p(x₀,...,x_p):=(A₀(x₀),A₁(x₀,x₁),...,A_p(x₀,...,x_p)), is a (weakly) Picard operator.