## On $$\alpha$$-condensing mappings in Banach algebras.(English)Zbl 0882.47033

Summary: A fixed point theorem involving two operators is proved in Banach algebras using the measure of noncompactness. An application is given to prove the existence theorem for nonlinear integral equations which include Volterra and Urysohn integral equations as special cases.

### MSC:

 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems