## Abstract

The purpose of this paper is to study an approximation method for finding a solution of the split minimization problem which is also a fixed point of a right Bregman strongly nonexpansive mapping in p-uniformly convex real Banach spaces which are also uniformly smooth. We introduce a new iterative algorithm with a new choice of stepsize such that its implementation does not require a prior knowledge of the operator norm. Using the Bregman distance technique, we prove a strong convergence theorem for the sequence generated by our algorithm. Further, we applied our result to the approximation of solution of inverse problem arising in signal processing and give a numerical example to show how the sequence values are affected by the number of iterations. Our result in this paper extends and complements many recent results in literature.

Original language | English |
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Pages (from-to) | 3-30 |

Number of pages | 28 |

Journal | Buletinul Academiei de Stiinte a Republicii Moldova. Matematica |

Volume | 95-96 |

Issue number | 1-2 |

Publication status | Published - 2021 |

Externally published | Yes |

## Keywords

- Banach spaces
- Bregman distance
- fixed point problems
- inverse problems
- proximal operators
- soft thresholding
- split feasibility problems
- split minimization problems