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- 저자 : Shahza, Mohammad (검색결과 2 건)
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TWO STEP ALGORITHM FOR SOLVING REGULARIZED GENERALIZED MIXED VARIATIONAL INEQUALITY PROBLEM
Kazmi, Kaleem Raza,Khan, Faizan Ahmad,Shahza, Mohammad Korean Mathematical Society 2010 대한수학회보 Vol.47 No.4
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].
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TWO STEP ALGORITHM FOR SOLVING REGULARIZED GENERALIZED MIXED VARIATIONAL INEQUALITY PROBLEM
Kaleem Raza Kazmi,Faizan Ahmad Khan,Mohammad Shahza 대한수학회 2010 대한수학회보 Vol.47 No.4
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 Θ-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 Θ-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].
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