General Strongly Nonlinear Quasivariational Inequalities with Relaxed Lipschitz and Relaxed Monotone Mappings |
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| Authors: | Liu Z. Ume J.S. Kang S.M. |
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| Affiliation: | (1) Department of Mathematics, Liaoning Normal University, Dalian, Liaoning, PRC;(2) Department of Applied Mathematics, Changwon National University, Changwon, Korea;(3) Department of Mathematics, Gyeongsang National University, Chinju, Korea |
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| Abstract: | In this paper, we introduce and study a new class of general strongly nonlinear quasivariational inequalities and construct a general iterative algorithm by using the projection method. We establish the existence of a unique solution for general strongly nonlinear quasivariational inequalities involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings; we obtain the convergence and stability of the iterative sequences generated by the algorithm. Our results extend, improve, and unify many known results due to Bose, Noor, Siddiqi-Ansari, Verma, Yao, Zeng, and others. |
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| Keywords: | general strongly nonlinear quasivariational inequalities projection methods relaxed Lipschitz mappings relaxed monotone mappings strongly monotone mappings Noor iterative scheme with errors stability |
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