Condensing mappings and applications to existence theorems for common solution of differential equations. (English) Zbl 0940.47043

Dhage, B. C.

Bull. Korean Math. Soc. 36, No. 3, 565-578 (1999).

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

Keywords:

existence theorem; common fixed point theorems; pairs of condensing mappings in a Banach space; nonlinear first-order ordinary differential equations in Banach spaces; common solution