Modified double two-step inertial hybrid projection algorithms with two iterative sequences for solving common fixed point problems
DOI:
https://doi.org/10.66147/lnaa.20264386Keywords:
Fixed point problem, Double two-step inertial method, Hybrid projection algorithm, Strong convergence, Numerical analysis.Abstract
This paper is dedicated to the study of common fixed point problem of nonexpansive mappings. Using the double two-step inertial method and hybrid projection algorithm, we design a modified double two-step inertial hybrid projection algorithm with two iterative sequences, and thus, a new variant of the hybrid projection algorithm is obtained. Then the previous two historical information of the two iterative sequences in the algorithm are further utilized simultaneously. Interestingly, a new and extended lemma tool is presented, it generalizes the known tools. This lemma tool plays an important role on the subsequent discussion in this paper. We utiliz this lemma to establish the strong convergence theorem of the proposed algorithm. To further verify the obtained results, two simple numerical experiments are provided. The conclusions obtained in this paper generalize and extend some previous results.
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