### Abstract

We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for continuous monotone mapping, solution of equilibrium problem and a common fixed point of finite family of asymptotically regular uniformly continuous relatively asymptotically nonexpansive mappings in Banach spaces. Our scheme does not involve computation of C_{n+1} from C_{n} for each n ≥ 1. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

Original language | English |
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Article number | 119 |

Journal | Fixed Point Theory and Applications |

Volume | 2012 |

DOIs | |

Publication status | Published - Dec 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Geometry and Topology
- Applied Mathematics

### Cite this

*Fixed Point Theory and Applications*,

*2012*, [119]. https://doi.org/10.1186/1687-1812-2012-119

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*Fixed Point Theory and Applications*, vol. 2012, 119. https://doi.org/10.1186/1687-1812-2012-119

**Strong convergence theorems for a common point of solution of variational inequality, solutions of equilibrium and fixed point problems.** / Zegeye, Habtu; Shahzad, Naseer; Alghamdi, Mohammad Ali.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Strong convergence theorems for a common point of solution of variational inequality, solutions of equilibrium and fixed point problems

AU - Zegeye, Habtu

AU - Shahzad, Naseer

AU - Alghamdi, Mohammad Ali

PY - 2012/12/1

Y1 - 2012/12/1

N2 - We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for continuous monotone mapping, solution of equilibrium problem and a common fixed point of finite family of asymptotically regular uniformly continuous relatively asymptotically nonexpansive mappings in Banach spaces. Our scheme does not involve computation of Cn+1 from Cn for each n ≥ 1. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

AB - We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for continuous monotone mapping, solution of equilibrium problem and a common fixed point of finite family of asymptotically regular uniformly continuous relatively asymptotically nonexpansive mappings in Banach spaces. Our scheme does not involve computation of Cn+1 from Cn for each n ≥ 1. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

UR - http://www.scopus.com/inward/record.url?scp=84872006136&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872006136&partnerID=8YFLogxK

U2 - 10.1186/1687-1812-2012-119

DO - 10.1186/1687-1812-2012-119

M3 - Article

VL - 2012

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

SN - 1687-1820

M1 - 119

ER -