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Condensing mappings and applications to existence theorems for common solution of differential equations. (English) Zbl 0940.47043
Summary: Some common fixed point theorems for pairs of condensing mappings in a Banach space are proved and applications are given to a pair of nonlinear first-order ordinary differential equations in Banach spaces for proving the existence of common solution under suitable conditions.

MSC:
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions