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 Two step algorithm for solving regularized generalized mixed variational inequality problem Bull. Korean Math. Soc. 2010 Vol. 47, No. 4, 675-685 https://doi.org/10.4134/BKMS.2010.47.4.675Published online July 1, 2010 Kaleem Raza Kazmi, Faizan Ahmad Khan, and Mohammad Shahza Aligarh Muslim University, Aligarh Muslim University, Aligarh Muslim University Abstract : In this paper, we consider a new class of regularized (nonconvex) generalized mixed variational inequality problems in real Hilbert space. We give the concepts of partially relaxed strongly mixed monotone and partially relaxed strongly $\theta$-pseudomonotone mappings, which are extension of the concepts given by Xia and Ding [19], Noor [13] and Kazmi et al. [9]. Further we use the auxiliary principle technique to suggest a two-step iterative algorithm for solving regularized (nonconvex) generalized mixed variational inequality problem. We prove that the convergence of the iterative algorithm requires only the continuity, partially relaxed strongly mixed monotonicity and partially relaxed strongly $\theta$-pseudomonotonicity. The theorems presented in this paper represent improvement and generalization of the previously known results for solving equilibrium problems and variational inequality problems involving the nonconvex (convex) sets, see for example Noor [13], Pang et al. [14], and Xia and Ding [19]. Keywords : regularized generalized mixed variational inequality problem, auxiliary problem, two-step iterative algorithm, convergence analysis, partially relaxed strongly mixed monotone mapping, regularized partially relaxed strongly $\theta$-pseudomonotone mapping, MSC numbers : 49J30, 90C30 Downloads: Full-text PDF