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Lobachevskii Journal of Mathematics

, Volume 35, Issue 4, pp 371–383 | Cite as

Iterative methods for solving variational inequalities of the theory of soft shells

Article

Abstract

The convergence of iterative methods for solving variational inequalities with monotone-type operators in Banach spaces is studied. Such inequalities arise in the description of deformation processes of soft rotational network shells. Certain properties of these operators, such as coercivity, potentiality, bounded Lipschitz continuity, pseudomonotonicity, and inverse strong monotonicity, are determined. An iterative method for solving these variational inequalities is proposed, its convergence is investigated, and the boundedness of the iterative sequence is proved. Moreover, it is proved that any weakly convergent subsequence of the iterative sequence converges to a solution of the original variational inequality.

Keywords and phrases

variational inequality pseudomonotone operator potential operator iterative method soft network shell 

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanTatarstan, Russia

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