## Abstract

In this paper, we introduce a modified Halpern algorithm for approximating a common solution of split equality convex minimization problem and split-equality fixed-point problem for Bregman quasi-nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We introduce a generalized step size such that the algorithm does not require a prior knowledge of the operator norms and prove a strong convergence theorem for the sequence generated by our algorithm. We give some applications and numerical examples to show the consistency and accuracy of our algorithm. Our results complement and extend many other recent results in this direction in literature.

Original language | English |
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Article number | 77 |

Journal | Computational and Applied Mathematics |

Volume | 38 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jun 2019 |

Externally published | Yes |

## Keywords

- Bregman quasi-nonexpansive
- Fixed point problem
- Minimization problem
- Proximal operator
- Split equality problem
- Split feasibility problem