Modified Hybrid Steepest Method for the Split Feasibility Problem in Image Recovery of Inverse Problems

ABSTRACT In this paper, we regard the CQ algorithm as a fixed point algorithm for averaged mapping, and also try to study the split feasibility problem by the following hybrid steepest method; where {αn}⊂(0,1). It is noted that Xu’s original iterative method can conclude only weak convergence. Consequently, we obtain the sequence {xn} generated by our iteration method converges strongly to , where is the unique solution of the variational inequality Our result extends and improves the result of Xu, as shown in the literature, from weak to strong convergence theorems. Finally, in the last section, numerical examples for study behavior convergence analysis of this algorithm are obtained.

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