##
**General convergence analysis for two-step projection methods and applications to variational problems.**
*(English)*
Zbl 1099.47054

Projection methods have played a signigicant role in the numerical resolution of variational inequalities based on their convergence analysis. In this paper, the author introduces general two-step projection methods and then applies them to the approximation solvability of a two-step strongly monotonic nonlinear variational inequality in a Hilbert space setting.

Editorial remark: See also [A. Benhadid, J. Prime Res. Math. 18, No. 1, 38–42 (2022; Zbl 07549710)].

Editorial remark: See also [A. Benhadid, J. Prime Res. Math. 18, No. 1, 38–42 (2022; Zbl 07549710)].

Reviewer: Jeon Sheok Ume (Changwon)

### MSC:

47J20 | Variational and other types of inequalities involving nonlinear operators (general) |

47J25 | Iterative procedures involving nonlinear operators |

### Keywords:

general two-step model; system of strongly monotonic nonlinear variational inequalities; projection methods; convergence of two-step projection methods### Citations:

Zbl 07549710
PDF
BibTeX
XML
Cite

\textit{R. U. Verma}, Appl. Math. Lett. 18, No. 11, 1286--1292 (2005; Zbl 1099.47054)

Full Text:
DOI

### References:

[1] | Dunn, J.C., Convexity, monotonicity and gradient processes in Hilbert spaces, Journal of mathematical analysis and applications, 53, 145-158, (1976) · Zbl 0321.49025 |

[2] | Verma, R.U., A class of quasivariational inequalities involving cocoercive mappings, Advances in nonlinear variational inequalities, 2, 2, 1-12, (1999) · Zbl 1007.49512 |

[3] | Verma, R.U., Generalized class of partial relaxed monotonicity and its connections, Advances in nonlinear variational inequalities, 7, 2, 155-164, (2004) · Zbl 1079.49011 |

[4] | Verma, R.U., Projection methods, algorithms and a new system of nonlinear variational inequalities, Computers & mathematics with applications, 41, 1025-1031, (2001) · Zbl 0995.47042 |

[5] | Nie, H.; Liu, Z.; Kim, K.H.; Kang, S.M., A system of nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings, Advances in nonlinear variational inequalities, 6, 2, 91-99, (2003) · Zbl 1098.47055 |

[6] | He, B.S., A new method for a class of linear variational inequalities, Mathematical programming, 66, 137-144, (1994) · Zbl 0813.49009 |

[7] | Karamardian, S.; Schaible, S., Seven kinds of monotone maps, Journal of optimization theory and applications, 66, 37-46, (1990) · Zbl 0679.90055 |

[8] | Kinderlehrer, D.; Stampacchia, G., An introduction to variational inequalities and their applications, (1980), Academic Press New York · Zbl 0457.35001 |

[9] | Verma, R.U., Nonlinear variational and constrained hemivariational inequalities involving relaxed operators, Zeitschrift für angewandte Mathematik und mechanik, 77, 5, 387-391, (1997) · Zbl 0886.49006 |

[10] | Wittmann, R., Approximation of fixed points of nonexpansive mappings, Archiv der Mathematik, 58, 486-491, (1992) · Zbl 0797.47036 |

[11] | Zeidler, E., Nonlinear functional analysis and its applications II/B, (1990), Springer-Verlag New York |

[12] | Zeidler, E., Nonlinear functional analysis and its applications I, (1986), Springer-Verlag New York |

[13] | Zhu, D.; Marcotte, P., New classes of generalized monotonicity, Journal of optimization theory and applications, 87, 2, 457-471, (1995) · Zbl 0837.65067 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.