## Abstract

The main purpose of this paper is to introduce a parallel iterative algorithm for approximating the solution of a split feasibility problem on the zero of monotone operators, generalized mixed equilibrium problem and fixed point problem. Using our algorithm, we state and prove a strong convergence theorem for approximating a common element in the set of solutions of a problem of finding zeroes of sum of two monotone operators, generalized mixed equilibrium problem and fixed point problem for a finite family of η-demimetric mappings in the frame work of a reflexive, strictly convex and smooth Banach spaces. We also give a numerical experiment applying our main result. Our result improves, extends and unifies other results in this direction in the literature.

Original language | English |
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Journal | Boletim da Sociedade Paranaense de Matematica |

Volume | 41 |

DOIs | |

Publication status | Published - 2023 |

Externally published | Yes |

## Keywords

- Banach space
- Split generalized mixed equilibrium problem
- monotone mapping
- parallel algorithm
- quasi-φ-nonexpansive mapping
- strong convergence