## Abstract

The purpose of this paper is to introduce iterative method for solving generalized split inverse problem given as a task of finding a point which belongs to the intersection of finite family of fixed point sets of demimetric mappings such that its image under a finite number of linear transformations belongs to the intersection of another finite family of fixed point sets of demimetric mappings in the image space. The proposed algorithm is formulated in low-cost sequential computing method with step size selection technique. The strong convergence theorem of the proposed algorithm is derived under the appropriate assumptions. The result presented in the paper generalized several results in the literature. Numerical example is given to illustrate the efficiency and performance of the proposed iterative method.

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## Acknowledgements

The author would like to thank the Associate Editor and anonymous reviewers for their comments and suggestions on improving an earlier version of this paper.

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Communicated by Natasa Krejic.

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Gebrie, A.G. A novel low-cost method for generalized split inverse problem of finite family of demimetric mappings.
*Comp. Appl. Math.* **40, **40 (2021). https://doi.org/10.1007/s40314-021-01437-2

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### Keywords

- Split inverse problem
- Demimetric mapping
- Fixed point
- Self-adaptive technique

### Mathematics Subject Classification

- 47J25
- 47H09
- 47H10
- 90C25