On Two Iterative Methods for Mixed Monotone Variational Inequalities

On Two Iterative Methods for Mixed Monotone Variational Inequalities

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A mixed monotone variational inequality (MMVI) problem gotrax handlebar in a Hilbert space H is formulated to find a point u∗∈H such that 〈Tu∗,v−u∗〉+φ(v)−φ(u∗)≥0 for all v∈H, where T is a monotone operator and φ is a proper, convex, and lower semicontinuous function on H.Iterative algorithms are usually applied to find a solution of an MMVI problem.We show that the iterative algorithm introduced in the work of Wang et al., (2001) has in general weak convergence in seattle seahawks socks an infinite-dimensional space, and the algorithm introduced in the paper of Noor (2001) fails in general to converge to a solution.