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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2013, Volume 155, Book 2, Pages 18–32 (Mi uzku1194)  

Iterative Methods for Solving Variational Inequalities of the Theory of Soft Shells

I. B. Badriev, V. V. Banderov

Kazan (Volga Region) Federal University

Abstract: In this paper we study the convergence of iterative methods for solving variational inequalities with monotone-type operators in Banach spaces. Such inequalities arise in the description of the deformation processes of soft network rotational shells. We establish the properties of these operators, i.e. coercivity, potentiality, bounded Lipschitz continuity, and pseudomonotonicity or inverse strong monotonicity. For solving these variational inequalities, we consider an iterative method, investigate its convergence, prove the boundedness of the iterative sequence, and establish that each its weakly convergent subsequence has as a limit the solution of the original variational inequality.

Keywords: variational inequality, pseudo-monotone operator, potential operator, iterative method, soft network shell.

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UDC: 517.957
Received: 15.04.2013

Citation: I. B. Badriev, V. V. Banderov, “Iterative Methods for Solving Variational Inequalities of the Theory of Soft Shells”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 155, no. 2, Kazan University, Kazan, 2013, 18–32

Citation in format AMSBIB
\Bibitem{BadBan13}
\by I.~B.~Badriev, V.~V.~Banderov
\paper Iterative Methods for Solving Variational Inequalities of the Theory of Soft Shells
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2013
\vol 155
\issue 2
\pages 18--32
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1194}


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