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TWO STEP ALGORITHM FOR SOLVING REGULARIZED GENERALIZED MIXED VARIATIONAL INEQUALITY PROBLEM
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 Title & Authors
TWO STEP ALGORITHM FOR SOLVING REGULARIZED GENERALIZED MIXED VARIATIONAL INEQUALITY PROBLEM
Kazmi, Kaleem Raza; Khan, Faizan Ahmad; Shahza, Mohammad;
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 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 -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 -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 -pseudomonotone mapping;skew-symmetric function;
 Language
English
 Cited by
1.
Existence Results for Vector Mixed Quasi-Complementarity Problems, Journal of Mathematics, 2013, 2013, 1  crossref(new windwow)
2.
Implicit iterative method for approximating a common solution of split equilibrium problem and fixed point problem for a nonexpansive semigroup, Arab Journal of Mathematical Sciences, 2014, 20, 1, 57  crossref(new windwow)
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