Strong convergence theorem for approximating zero of accretive operators and application to Hammerstein equation

Let C be a nonempty, closed and convex subset of a real q-uniformly smooth Banach space X which admits a weakly sequentially continuous generalized duality mapping jq. We study the approximation of the zero of a strongly accretive operator A: X →X which is also the fixed point of a k strictly pseudo-contractive self mapping on C. We introduce a new algorithm and prove its strong convergence to the zero of A and fixed point of T. The obtained result is applied to the solution of nonlinear integral equation of the Hammerstein type. Our result extends some existing results in literature.