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

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.