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

Abstract

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 $j_q$. We study the approximation of the zero of a strongly accretive operator $A: X \to X$ 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.