Journal of Mathematical Inequalities

(communicated by Th. Rassias) Abstract. In this paper, we suggest and analyze some new iterative methods for finding the fixed point of nonexpansive mapping in Banach spaces, which are called modified Noor iterations. We show that the approximate solution converges to a fixed point of the nonexpansive mapping, which is a solution of a variational inequality, under some mild conditions. Results obtained in this paper may be viewed as a significant refinement of the previously known results in this area. 1