## Abstract

We consider a system of pseudomonotone equilibrium problem and split common fixed point problem in the framework of real Hilbert spaces. We propose a modified extragradient method with line searching technique for approximating a common element in the sets of solutions of the two nonlinear problems. The convergence result is proved without prior knowledge of the Lipschitz-like constants of the equilibrium bifunctions and the norm of the bounded linear operator of the split common fixed point problem. We further provide some application and numerical example to show the importance of the obtained results in the paper.

Original language | English |
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Pages (from-to) | 403-428 |

Number of pages | 26 |

Journal | Bolletino dell Unione Matematica Italiana |

Volume | 14 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2021 |

## Keywords

- Demimetric mappings
- Equilibrum problem
- Parallel algorithm
- Pseudomonotone equilibrium
- Split common fixed point
- numerical method