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This paper introduces a triple-adaptive subgradient extragradient process with extrapolation to solve a bilevel split pseudomonotone variational inequality problem (BSPVIP) with the common fixed point problem constraint of finitely many nonexpansive mappings. The problem under consideration is in real Hilbert spaces, where the BSPVIP involves a fixed point problem of demimetric mapping. The proposed rule exploits the strong monotonicity of one operator at the upper level and the pseudomonotonicity of another mapping at the lower level. The strong convergence result for the proposed algorithm is established under some suitable assumptions. In addition, a numerical example is given to demonstrate the viability of the proposed rule. Our results improve and extend some recent developments to a great extent. [ABSTRACT FROM AUTHOR]

In a real Hilbert space, let the VIP, GSVI, HVI, and CFPP denote a variational inequality problem, a general system of variational inequalities, a hierarchical variational inequality, and a common fixed-point problem of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping, respectively. We design two Mann implicit composite subgradient extragradient algorithms with line-search process for finding a common solution of the CFPP, GSVI, and VIP. The suggested algorithms are based on the Mann implicit iteration method, subgradient extragradient method with line-search process, and viscosity approximation method. Under mild assumptions, we prove the strong convergence of the suggested algorithms to a common solution of the CFPP, GSVI, and VIP, which solves a certain HVI defined on their common solutions set. [ABSTRACT FROM AUTHOR]

In this paper, using a Bregman distance technique, we introduce a new single projection process for approximating a common element in the set of solutions of variational inequalities involving a pseudo-monotone operator and the set of common fixed points of a finite family of Bregman quasi-nonexpansive mappings in a real reflexive Banach space. The stepsize of our algorithm is determined by a self-adaptive method, and we prove a strong convergence result under certain mild conditions. We further give some applications of our result to a generalized Nash equilibrium problem and bandwidth allocation problems. We also provide some numerical experiments to illustrate the performance of our proposed algorithm using various convex functions and compare this algorithm with other algorithms in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in Banach spaces and equilibrium problems in Hilbert spaces. Finally, we give some numerical examples for supporting our main results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of gap functions of random generalized variational inequality problems in a fuzzy environment. Further by using the residual vector we compute error bounds for random generalized variational inequality problems and we generalize the regularized gap functions proposed by Fukushima. Furthermore we study various properties of the generalized regularized gap functions in random fuzzy mappings and derive the global error bounds for random generalized variational inequality problems. Our results are new and generalize a number of known results to generalized variational inequality problems with fuzzy mappings. [ABSTRACT FROM AUTHOR]

In this paper, we define some new notions of gap functions for set-valued mixed quasi-variational inequalities under suitable conditions. Further, we obtain local/global bounds for the solution of set-valued mixed quasi-variational inequality problems in terms of the residual gap function, the regularized gap function, and the D-gap function. The results obtained in this paper are generalization and refinement of previously known results for some class of variational inequality problems. [ABSTRACT FROM AUTHOR]