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TWO STEP ALGORITHM FOR SOLVING REGULARIZED GENERALIZED MIXED VARIATIONAL INEQUALITY PROBLEM
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  • TWO STEP ALGORITHM FOR SOLVING REGULARIZED GENERALIZED MIXED VARIATIONAL INEQUALITY PROBLEM
  • TWO STEP ALGORITHM FOR SOLVING REGULARIZED GENERALIZED MIXED VARIATIONAL INEQUALITY PROBLEM
저자명
Kazmi. Kaleem Raza,Khan. Faizan Ahmad,Shahza. Mohammad
간행물명
Bulletin of the Korean Mathematical Society
권/호정보
2010년|47권 4호|pp.675-685 (11 pages)
발행정보
대한수학회
파일정보
정기간행물|ENG|
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이 논문은 한국과학기술정보연구원과 논문 연계를 통해 무료로 제공되는 원문입니다.
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기타언어초록

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 $ heta$-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 $ heta$-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].