Split equality variational inequality problems for pseudomonotone mappings in Banach spaces

"A new algorithm for approximating solutions of the split equality variational inequality problems (SEVIP) for pseudomonotone mappings in the setting of Banach spaces is introduced. Strong convergence of the sequence generated by the proposed algorithm to a solution of the SEVIP is then derived without assuming the Lipschitz continuity of the underlying mappings and without prior knowledge of operator norms of the bounded linear operators involved. In addition, we provide several applications of our method and provide a numerical example to illustrate the convergence of the proposed algorithm. Our results improve, consolidate and complement several results reported in the literature."

Hemivariational inequalities modeling electro-elastic unilateral frictional contact problem

We study a class of abstract hemivariational inequalities in a reflexive Banach space. For this class, using the theory of multivalued pseudomonotone mappings and a fixed-point argument, we provide a result on the existence and uniqueness of the solution. Next, we investigate a static frictional contact problem with unilateral constraints between a piezoelastic body and a conductive foundation. The contact, friction and electrical conductivity condition on the contact surface are described with the Clarke generalized subgradient multivalued boundary relations. We derive the variational formulation of the contact problem which is a coupled system of two hemivariational inequalities. Finally, for such system we apply our abstract result and prove its unique weak solvability.