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An iterative scheme for split equality equilibrium problems and split equality hierarchical fixed point problem
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DOI：10.1186/s13662-021-03384-y.png)
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Abstract
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This paper deals with a split equality equilibrium problem for pseudomonotone bifunctions and a split equality hierarchical fixed point problem for nonexpansive and quasinonexpansive mappings. We suggest and analyze an iterative scheme where the stepsizes do not depend on the operator norms, the so-called simultaneous projected subgradient-proximal iterative scheme for approximating a common solution of the split equality equilibrium problem and the split equality hierarchical fixed point problem. Further, we prove a weak convergence theorem for the sequences generated by this scheme. Furthermore, we discuss some consequences of the weak convergence theorem. We present a numerical example to justify the main result.
Keywords:
Split equality equilibrium problem
Split equality hierarchical fixed point problem
Simultaneous hybrid projected subgradient-proximal iterative scheme
Quasinonexpansive mapping
Pseudomonotone bifunction
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