Convergence analysis of multiple-sets split equality common fixed point problem with applications

Abstract

In this paper, we suggest a new inertial type parallel iterative algorithm and prove its strong convergence for finding a solution of multiple-sets split equality common fixed point problem for a finite family of demicontractive mappings in real Hilbert spaces. The suggested algorithm does not require prior knowledge of operator norm. We apply our result to study multiple-sets split equality common fixed point problem for a finite family of quasi-pseudocontractive mappings. Further, we also apply our result to solve various split type problems and intensity-modulated radiation therapy. Moreover, we give numerical experiments for supporting our main result and compare it with other existing methods.