Algorithm for Hammerstein equations with monotone mappings in certain Banach spaces

For and , let be a 2-uniformly convex and -uniformly smooth or – uniformly convex and
-uniformly smooth real Banach space and , be bounded and strongly monotone maps with . We construct a coupled iterative process and prove its  strong convergence to a solution of the Hammerstein equation .  Futhermore, our technique of proof is of independent of interest.