### Abstract

In this paper we consider the problem of minimizing a non necessarily differentiable convex function over the intersection of fixed point sets associated with an infinite family of multivalued quasi-nonexpansive mappings in a real Hilbert space. The new algorithm allows us to solve problems when the mappings are not necessarily projection operators or when the computation of projections is not an easy task. The a priori knowledge of operator norms is avoided and conditions to get the strong convergence of the new algorithm are given. Finally the particular case of split equality fixed point problems for family of multivalued mappings is displayed. Our general algorithm can be considered as an extension of Shehu’s method to a larger class of problems.

Original language | English |
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Pages (from-to) | 983-998 |

Number of pages | 16 |

Journal | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas |

Volume | 111 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Oct 2017 |

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### Keywords

- Demiclosed operator
- Multiple-set split equality fixed point problem
- Quasi-nonexpansive operator
- Strong convergence

### Cite this

*Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas*,

*111*(4), 983-998. https://doi.org/10.1007/s13398-016-0338-7

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*Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas*, vol. 111, no. 4, pp. 983-998. https://doi.org/10.1007/s13398-016-0338-7

**Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space.** / Giang, Dinh Minh; Strodiot, Jean Jacques; Nguyen, Van Hien.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space

AU - Giang, Dinh Minh

AU - Strodiot, Jean Jacques

AU - Nguyen, Van Hien

PY - 2017/10/1

Y1 - 2017/10/1

N2 - In this paper we consider the problem of minimizing a non necessarily differentiable convex function over the intersection of fixed point sets associated with an infinite family of multivalued quasi-nonexpansive mappings in a real Hilbert space. The new algorithm allows us to solve problems when the mappings are not necessarily projection operators or when the computation of projections is not an easy task. The a priori knowledge of operator norms is avoided and conditions to get the strong convergence of the new algorithm are given. Finally the particular case of split equality fixed point problems for family of multivalued mappings is displayed. Our general algorithm can be considered as an extension of Shehu’s method to a larger class of problems.

AB - In this paper we consider the problem of minimizing a non necessarily differentiable convex function over the intersection of fixed point sets associated with an infinite family of multivalued quasi-nonexpansive mappings in a real Hilbert space. The new algorithm allows us to solve problems when the mappings are not necessarily projection operators or when the computation of projections is not an easy task. The a priori knowledge of operator norms is avoided and conditions to get the strong convergence of the new algorithm are given. Finally the particular case of split equality fixed point problems for family of multivalued mappings is displayed. Our general algorithm can be considered as an extension of Shehu’s method to a larger class of problems.

KW - Demiclosed operator

KW - Multiple-set split equality fixed point problem

KW - Quasi-nonexpansive operator

KW - Strong convergence

UR - http://www.scopus.com/inward/record.url?scp=85028373276&partnerID=8YFLogxK

U2 - 10.1007/s13398-016-0338-7

DO - 10.1007/s13398-016-0338-7

M3 - Article

VL - 111

SP - 983

EP - 998

JO - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

JF - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas

SN - 1578-7303

IS - 4

ER -