Algorithm for the solution of Hammerstein integral typ e of equation in a Banach Spaces

Abstract This pap er investigates the convergence of iterative methods for solving functional equations of the form u + KF u = 0 in a normed linear space E. The equations under consideration include nonlinear integral equations of Hammerstein type, where F and K are maps between E and its dual E∗. The article explores diffrent extensions of monotonicity and accretivity concepts for operators in Banach spaces and highlighting their connections with minimax theory. Building upon previous results on iterative approximation schemes, we present new iterative algorithms that yield strong convergence to the unique solution of the Hammerstein equation.