# On split inclusion problem and fixed point problem for multi-valued mappings

## Abstract

Many of the iterative schemes for solving split inclusion and fixed point problems involve step-sizes that depend on the norm of a bounded linear operator. The implementation of such algorithms are usually difficult to handle. This is because they require the computation of the operator norm. In this paper, we propose an algorithm involving a step-size selected in such a way that its implementation does not require the computation or an estimate of some spectral radius. Using our algorithm we proved strong convergence theorem for split inclusion problem and fixed point problem for multi-valued quasi-nonexpansive mappings in real Hilbert spaces. Our result generalizes some important and recent results in the literature. Some applications of our main result to game theory and variational inequality problem are also presented.

- Authors:

- University of Nigeria, Department of Mathematics (Nigeria)

- Publication Date:

- OSTI Identifier:
- 22769328

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; CONVERGENCE; GAME THEORY; HILBERT SPACE; ITERATIVE METHODS; VARIATIONAL METHODS

### Citation Formats

```
Shehu, Yekini, and Agbebaku, Dennis F., E-mail: dennis.agbebaku@unn.edu.ng.
```*On split inclusion problem and fixed point problem for multi-valued mappings*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0426-0.

```
Shehu, Yekini, & Agbebaku, Dennis F., E-mail: dennis.agbebaku@unn.edu.ng.
```*On split inclusion problem and fixed point problem for multi-valued mappings*. United States. doi:10.1007/S40314-017-0426-0.

```
Shehu, Yekini, and Agbebaku, Dennis F., E-mail: dennis.agbebaku@unn.edu.ng. Tue .
"On split inclusion problem and fixed point problem for multi-valued mappings". United States. doi:10.1007/S40314-017-0426-0.
```

```
@article{osti_22769328,
```

title = {On split inclusion problem and fixed point problem for multi-valued mappings},

author = {Shehu, Yekini and Agbebaku, Dennis F., E-mail: dennis.agbebaku@unn.edu.ng},

abstractNote = {Many of the iterative schemes for solving split inclusion and fixed point problems involve step-sizes that depend on the norm of a bounded linear operator. The implementation of such algorithms are usually difficult to handle. This is because they require the computation of the operator norm. In this paper, we propose an algorithm involving a step-size selected in such a way that its implementation does not require the computation or an estimate of some spectral radius. Using our algorithm we proved strong convergence theorem for split inclusion problem and fixed point problem for multi-valued quasi-nonexpansive mappings in real Hilbert spaces. Our result generalizes some important and recent results in the literature. Some applications of our main result to game theory and variational inequality problem are also presented.},

doi = {10.1007/S40314-017-0426-0},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}