Yi-bin Xiao

Browder-Tikhonov regularization for a class of evolution second order hemivariational inequalities

In this paper, we consider a class of evolution second order hemivariational inequalities with non-coercive operators which are assumed to be known approximately. Using the so-called Browder-Tikhonov regularization method, we prove that the regularized evolution hemivariational inequality problem is solvable. We construct a sequence based on the solvability of the regularized evolution hemivariational inequality problem and show that every weak cluster of this sequence is a solution for the evolution second order hemivariational inequality.

Fully history-dependent quasivariational inequalities in contact mechanics

In this paper, we consider a new class of fully history-dependent quasivariational inequalities which arise in the study of quasistatic models of contact and involve two history-dependent operators. By using a fixed-point theorem and arguments of monotonicity and convexity, we prove an existence and uniqueness result of the solution, which includes as special cases some results already obtained in some papers. Then, the obtained result is applied to two problems of quasistatic frictional contact for viscoelastic materials and the unique weak solvability of each contact problem is obtained.

Well-posedness for a Class of Variational–Hemivariational Inequalities with Perturbations

In this paper, we consider an extension of well-posedness for a minimization problem to a class of variational–hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed variational–hemivariational inequality and give some conditions under which the variational–hemivariational inequality is strongly well-posed in the generalized sense. Under some mild conditions, we also prove the equivalence between the well-posedness of variational–hemivariational inequality and the well-posedness of corresponding inclusion problem.

A class of generalized evolution variational inequalities in Banach spaces

Abstract In the present paper, a class of generalized evolution variational inequalities arising in a number of quasistatic frictional contact problems for viscoelastic materials is introduced and studied. Using Banach’s fixed point theorem, the existence and uniqueness theorem of the solution for the generalized evolution variational inequalities is proved under some suitable assumptions.

Some equivalence results for well-posedness of hemivariational inequalities

In the present paper, we are devoted to exploring conditions of well-posedness for hemivariational inequalities in reflexive Banach spaces. By using some equivalent formulations of the hemivariational inequality considered under different monotonicity assumptions, we establish two kinds of conditions under which the strong well-posedness and the weak well-posedness for the hemivariational inequality considered are equivalent to the existence and uniqueness of its solution, respectively.

A Class of Delay Differential Variational Inequalities

In the paper, we introduce a class of delay differential variational inequalities consisting of a system of delay differential equations and variational inequalities. The existence conclusion of Carathéodory’s weak solution for delay differential variational equalities is obtained. Furthermore, an algorithm for solving the delay differential variational inequality is shown, and the convergence analysis for the algorithm is given. Finally, a numerical example is given to verify the validity of the algorithm.

A System of Time-Dependent Hemivariational Inequalities with Volterra Integral Terms

In this paper, we consider a system of time-dependent hemivariational inequalities with Volterra integral terms by using a surjectivity theorem for pseudomonotone operators and the Banach fixed point theorem, rather than the Knaster-Kuratowski-Mazurkiewicz theorems used by many researchers in recent literature for systems of hemivariational inequalities. Under some suitable conditions, the existence and uniqueness result of solution to the problem considered is obtained by proving that a derived vector inclusion problem with Volterra integral term is solvable.

New Characterization of Geodesic Convexity on Hadamard Manifolds with Applications

In this paper, some new results, concerned with the geodesic convex hull and geodesic convex combination, are given on Hadamard manifolds. An S-KKM theorem on a Hadamard manifold is also given in order to generalize the KKM theorem. As applications, a Fan–Browder-type fixed point theorem and a fixed point theorem for the a new mapping class are proved on Hadamard manifolds.

Modified extragradient algorithms for solving equilibrium problems

ABSTRACT In this paper, we introduce some new algorithms for solving the equilibrium problem in a Hilbert space which are constructed around the proximal-like mapping and inertial effect. Also, some convergence theorems of the algorithms are established under mild conditions. Finally, several experiments are performed to show the computational efficiency and the advantage of the proposed algorithm over other well-known algorithms.

A new projection-type method for solving multi-valued mixed variational inequalities without monotonicity

ABSTRACT In this paper, a new projection-type algorithm for solving multi-valued mixed variational inequalities without monotonicity is presented. Under some suitable assumptions, it is showed that the sequence generated by the proposed algorithm converges globally to a solution of the multi-valued mixed variational inequality considered. The algorithm exploited in this paper is based on the generalized f -projection operator due to Wu and Huang [The generalized f-projection operator with an application. Bull Austral Math Soc. 2006;73:307–317] rather than the well-known resolvent operator. Preliminary computational experience is also reported. The results presented in this paper generalize and improve some known results given in the literature.