### Abstract

In this paper, it is our aim to prove strong convergence of a new iterative algorithm to a common element of the set of solutions of a finite family of classical equilibrium problems; a common set of zeros of a finite family of inverse strongly monotone operators; the set of common fixed points of a finite family of quasi-nonexpansive mappings; and the set of common fixed points of a finite family of continuous pseudocontractive mappings in Hilbert spaces on assumption that the intersection of the aforementioned sets is not empty. Moreover, the common element is shown to be the metric projection of the initial guess on the intersection of these sets.

Original language | English |
---|---|

Article number | 9 |

Journal | Fixed Point Theory and Applications |

Volume | 2014 |

DOIs | |

Publication status | Published - Jan 1 2014 |

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### All Science Journal Classification (ASJC) codes

- Geometry and Topology
- Applied Mathematics

### Cite this

*Fixed Point Theory and Applications*,

*2014*, [9]. https://doi.org/10.1186/1687-1812-2014-9

}

*Fixed Point Theory and Applications*, vol. 2014, 9. https://doi.org/10.1186/1687-1812-2014-9

**An algorithm for finding common solutions of various problems in nonlinear operator theory.** / Ofoedu, Eric U.; Odumegwu, Jonathan N.; Zegeye, Habtu; Shahzad, Naseer.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An algorithm for finding common solutions of various problems in nonlinear operator theory

AU - Ofoedu, Eric U.

AU - Odumegwu, Jonathan N.

AU - Zegeye, Habtu

AU - Shahzad, Naseer

PY - 2014/1/1

Y1 - 2014/1/1

N2 - In this paper, it is our aim to prove strong convergence of a new iterative algorithm to a common element of the set of solutions of a finite family of classical equilibrium problems; a common set of zeros of a finite family of inverse strongly monotone operators; the set of common fixed points of a finite family of quasi-nonexpansive mappings; and the set of common fixed points of a finite family of continuous pseudocontractive mappings in Hilbert spaces on assumption that the intersection of the aforementioned sets is not empty. Moreover, the common element is shown to be the metric projection of the initial guess on the intersection of these sets.

AB - In this paper, it is our aim to prove strong convergence of a new iterative algorithm to a common element of the set of solutions of a finite family of classical equilibrium problems; a common set of zeros of a finite family of inverse strongly monotone operators; the set of common fixed points of a finite family of quasi-nonexpansive mappings; and the set of common fixed points of a finite family of continuous pseudocontractive mappings in Hilbert spaces on assumption that the intersection of the aforementioned sets is not empty. Moreover, the common element is shown to be the metric projection of the initial guess on the intersection of these sets.

UR - http://www.scopus.com/inward/record.url?scp=84899893946&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899893946&partnerID=8YFLogxK

U2 - 10.1186/1687-1812-2014-9

DO - 10.1186/1687-1812-2014-9

M3 - Article

VL - 2014

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

SN - 1687-1820

M1 - 9

ER -