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In this paper, four extragradient-type algorithms are presented for solving bilevel variational inequalities of pseudomonotone and non-Lipschitz continuous operators in real Hilbert spaces. The proposed iterative schemes employ two Armijo-type linesearch methods making them work adaptively. Strong convergence theorems of the suggested algorithms are established under some mild conditions. Finally, some numerical experiments and applications are given to verify the advantages and efficiency of the proposed algorithms over some previously known ones. [ABSTRACT FROM AUTHOR]

This article proposes two general inertial algorithms with line-search process for finding a solution of a variational inequality problem with fixed-point constraints via a subgradient-extragradient approach. Common solution theorems are obtained in Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a general composite implicit scheme and a general composite explicit scheme for finding a solution of general system of variational inequalities in a real Hilbert space. We establish the strong convergence of these two general composite schemes to a solution of the general system of variational inequalities which is the unique solution of some variational inequality. Applications to variational inequalities are given. [ABSTRACT FROM AUTHOR]

In this paper, we will consider coupled fixed point problems in b-metric spaces for single-valued operators satisfying a symmetric contraction condition. On one hand, existence and uniqueness of the solution and, on the other hand, data dependence, well-posedness, Ulam-Hyers stability, limit shadowing property of the coupled fixed point problem are discussed. The approach is based on the application of a Ran-Reurings type fixed point theorem for an appropriate operator on the Cartesian product space. Some applications to a system of integral equations and to a periodic boundary value problems are also given. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce hybrid pseudoviscosity approximation schemes with strongly positive bounded linear operators for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of infinitely many nonexpansive mappings in the setting of Hilbert spaces. We prove the strong convergence of the sequences generated by our scheme to a solution of an equilibrium problem which is also a common fixed point of infinitely many nonexpansive mappings. Our results can be treated as extension and improvement of the corresponding results appeared in the literature in the recent past. [Copyright &y& Elsevier]

Abstract: The present paper is divided into two parts. In the first part, we introduce implicit and explicit iterative schemes for finding the fixed point of a nonexpansive mapping defined on the closed convex subset of a real Hilbert space. We establish results on the strong convergence of the sequences generated by the proposed schemes to a fixed point of a nonexpansive mapping. Such a fixed point is also a solution of a variational inequality defined on the set of fixed points. In the second part, we propose implicit and explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem. Such a solution is also a solution of a variational inequality defined over the set of fixed points of a nonexpansive mapping. The results of this paper extend and improve several results presented in the literature in the recent past. [Copyright &y& Elsevier]