Generalized multivalued implicit variational inequalities involving the Verma class of mappings (Q2747461)

Let \(H\) be a real Hilbert space with the inner product \(\langle \cdot,\cdot\rangle\) and norm \(\|\cdot\|\). Let \(T:H\times H\to 2^H\) be a set-valued mapping and \(K\) be a nonempty closed convex subset of \(H\). The author considers a class of generalized set-valued implicit variational inequality problems of finding \(x^*\in K\) and \(u^*\in T(x^*,x^*)\) such that \(\langle u^*,x-x^*\rangle\geq 0\) for all \(x\in K\). He proves that the sequence generated by the algorithm converges to the solution of the generalized set-valued implicit variational inequality problem under the assumption that \(T\) satisfies some relaxed monotonicity conditions.