## 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:

 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations