Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations

Abstract

The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton’s method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper is to extend and improve some earlier results to nonlinear HTFIEs. The authors prove two new theorems with regard to the existence and uniqueness of solutions (EUSs) of HTFIEs via a technique called progressive contractions, which belongs to T. A. Burton, and the Chebyshev norm and complete metric.