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Abstract. In this paper we consider the general variational inequality GVI(F, g, C) where F and g are mappings from a Hilbert space into itself and C is the fixed points set of a nonexpansive mapping. We propose two iterative algorithms to find approximate solutions of the GVI (F, g, C). Strong convergence results are established and applications to constrained generalized pseudoinverse are included.

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Consider the following Kirchhoff type problemwhereN −2 and a, b, λ, µ are positive parameters. By introducing some new ideas and using the well-known results of the problem (P) in the cases of a = µ = 1 and b = 0, we obtain some special kinds of solutions to (P) for all N ≥ 3 with precise expressions on the parameters a, b, λ, µ, which reveals some new phenomenons of the solutions to the problem (P). It is also worth to point out that it seems to be the first time that the solutions of (P) can be expressed precisely on the parameters a, b, λ, µ, and our results in dimension four also give a partial answer to Neimen's open problems

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