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An iterative method for solution of finite families of split minimization problems and fixed point problems

The purpose of this paper is to introduce a proximal iterative algorithm for the approximation of a common solution of finite families of split minimization problem and a fixed point problem in the framework of Hilbert space. Using our iterative algorithm, we prove a strong convergence theorem for approximating a common solution of finite families of split minimization problem and a fixed point problem of nonexpansive mapping. Moreover, our result complements and extends some related results in literature.