Abstract
The present paper deals with the common solution method for finding a fixed point of a nonexpansive mapping and a solution of split hierarchical Minty variational inequality problems. We discuss the weak convergence of the sequences generated by the proposed method to a common solution of a fixed point problem and a split hierarchical Minty variational inequality problem. An example is presented to illustrate the proposed algorithm and result.
Highlights
Since its origin in by Censor and Elfving [ ], the split feasibility problem (SFP) has been rapidly investigated and studied because of its applications in different areas such as signal processing, phase retrievals, image reconstruction, intensity-modulated radiation therapy, etc
Moudafi [ ] further proposed and analyzed an iterative scheme for solving split common fixed point problem (SCFPP) for the class of demicontractive operators in the setting of Hilbert spaces. He studied the weak convergence of the sequence generated by the proposed algorithm to a solution of SCFPP
In, Moudafi [ ] considered the relaxed algorithm for computing the approximate solution of SCFPP for quasinonexpansive operators and studied the weak convergence of the sequence generated by the suggested algorithm
Summary
Since its origin in by Censor and Elfving [ ], the split feasibility problem (SFP) has been rapidly investigated and studied because of its applications in different areas such as signal processing, phase retrievals, image reconstruction, intensity-modulated radiation therapy, etc. (see, for example, [ – ] and the references therein). He studied the weak convergence of the sequence generated by the proposed algorithm to a solution of SCFPP. In , Moudafi [ ] considered the relaxed algorithm for computing the approximate solution of SCFPP for quasinonexpansive operators and studied the weak convergence of the sequence generated by the suggested algorithm.
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