A simplified homotopy perturbation method for solving nonlinear ill-posed operator equations in Hilbert spaces

One popular regularization technique for handling both linear and nonlinear ill-posed problems is homotopy perturbation. In order to solve nonlinear ill-posed problems, we investigate an iteratively-regularized simplified version of the Homotopy perturbation approach in this study. We examine the method's thorough convergence analysis under typical circumstances, focusing on the nonlinearity and the convergence rate under a H"{o}lder-type source condition. Lastly, numerical simulations are run to confirm the method's effectiveness.