Abstarct: In this thesis, we discuss the equation Ax = y on the Banach space with iterative method, where A is K-positive definite operator and k is a closed operator and continuous D(A)-inverse. Then we extend K-positive definite operator to Fréchet operator and we investigate local convergence towards unique equation Ax = y on Banach space. Also we introduce K-strong accretive that it is the nonlinear case of K-positive definite operator and we express results of the best approximation.