Hybrid Iterative Algorithm For A Class Of Optimization Problems With Fixed Point Constraints

The purpose of this paper is to study a hybrid iterative algorithm for a class of optimization problems with fixed point constraints in real Hilbert space.We propose an iterative algorithm to find a solution to the split feasible problem and the fixed point problem involving the Lipschitz pseudocontractive mappings.Under appropriate conditions,It is proved that the sequence generated by our iterative algorithm is weakly convergent to the split feasible problem.This paper improves and develops the existing results.This paper is divided into four parts.In the first chapter,it mainly introduces the research significance of split feasibility and the research status at home and abroad,and briefly describes the main research work of this paper.The second chapter is the introduction and the preparatory knowledge.The third chapter studies a kind of iterative algorithm to solve the split feasible problem and the fixed point problem,and gives the proof of its convergence.The fourth chapter is the conclusion and the prospect.