Abstract   

      The algorithms has a great role to find zeroes of metric projection point , fixed point and common fixed point in Hilbert space .It is well known that the metric projection mapping plays important role in Fixed point theory , Differential Equations, Optimization theory and Variational Inequality problem. The success, effectiveness, speed and superiority of iterative methods over other approximate methods depend on two important factors: The first is the number of iterations, and the second is time. In this paper, we introduce new iterative, it has been generalized to a number of algorithms, such as the algorithm used in27, which is considered a generalization of the Ishikawa's iteration algorithm. We use family of hybrid multivalued mappings, nonexpansive single valued mappings and (φ,L)^*- weak contraction mapping where φ is a comparison function in Hilbert space, the concept of (φ,L)^*- weak contraction mapping it is generalization of the concept (φ,L)- weak contraction mapping, we obtain several convergence theorems under suitable conditions.