The paper by Shiro Ishikawa presents a new iteration method to find fixed points of a Lipschitzian pseudo-contractive map in a Hilbert space. The method involves a sequence defined by \( x_{n+1} = \alpha_n T[\beta_n T x_n + (1 - \beta_n) x_n] + (1 - \alpha_n) x_n \), where \( \{\alpha_n\} \) and \( \{\beta_n\} \) are sequences of positive numbers satisfying specific conditions. The main result shows that this sequence converges strongly to a fixed point of the map \( T \). The proof uses properties of pseudo-contractive maps, the compactness of the domain, and the compactness of the set of fixed points. The author also acknowledges the contributions of Professors H. Fujita and T. Kawata for their suggestions.The paper by Shiro Ishikawa presents a new iteration method to find fixed points of a Lipschitzian pseudo-contractive map in a Hilbert space. The method involves a sequence defined by \( x_{n+1} = \alpha_n T[\beta_n T x_n + (1 - \beta_n) x_n] + (1 - \alpha_n) x_n \), where \( \{\alpha_n\} \) and \( \{\beta_n\} \) are sequences of positive numbers satisfying specific conditions. The main result shows that this sequence converges strongly to a fixed point of the map \( T \). The proof uses properties of pseudo-contractive maps, the compactness of the domain, and the compactness of the set of fixed points. The author also acknowledges the contributions of Professors H. Fujita and T. Kawata for their suggestions.