Hilbert空间上新的变分不等式问题和不动点问题的粘性迭代算法

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Hilbert空间上新的变分不等式问题和不动点问题的粘性迭代算法蔡钢重庆师范大学数学科学学院重庆 401331 Viscosity Iterative Algorithms for a New Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces Gang CAISchool of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China

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摘要本文在Hilbert空间上引入了一个新的粘性迭代算法，找到了关于两个逆强单调算子的变分不等式问题的解集与非扩张映射的不动点集的公共元.通过修改的超梯度算法，得到了强收敛定理，也给出了一个数值例子.所得结果改进了许多最新结果.

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收稿日期: 2019-02-10

MR (2010):

O177.91

基金资助:国家自然科学基金（11401063，11771063）；重庆市自然科学基金（cstc2017jcyjAX0006）；重庆市教委项目（KJ1703041）；重庆市高等学校青年骨干教师资助计划（020603011714）；重庆师范大学青年拔尖人才计划（02030307-00024）

作者简介: E-mail:caigang-aaaa@163.com}

引用本文:

蔡钢. Hilbert空间上新的变分不等式问题和不动点问题的粘性迭代算法[J]. 数学学报, 2019, 62(5): 765-776. Gang CAI. Viscosity Iterative Algorithms for a New Variational Inequality Problem and Fixed Point Problem in Hilbert Spaces. Acta Mathematica Sinica, Chinese Series, 2019, 62(5): 765-776.

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[1] Blum E., Oettli W., From optimization and variational inequalities to equilibrium problems, Math. Stud., 1994, 63:123-145.
[2] Ceng L. C., Wang C., Yao J. C., Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Methods Oper. Res., 2008, 67:375-390.
[3] Chang S. S., On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces, J. Math. Anal. Appl., 1997, 216:94-111.
[4] Colao V., Marino G., Xu H. K., An iterative method for finding common solutions of equilibrium and fixed point problems, J. Math. Anal. Appl., 2008, 344:340-352.
[5] Combettes P. L., Hirstoaga S. A., Equilibrium programming in Hilbert space, J. Nonlinear convex Anal., 2002, 6:117-136.
[6] Iiduka H., Takahashi W., Toyoda M., Approximation of solutions of variational inequalities for monotone mappings, Pan. Math. J., 2004, 14:49-61.
[7] Lim T. C., Xu H. K., Fixed point theorems for asymptotically nonexpansive mappings, Nonlinear Anal., 1994, 22:1345-1355.
[8] Marino G., Xu H. K., A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 2006, 318:43-52.
[9] Moudafi A., Viscosity approximation methods for fixed points problems, J. Math. Anal. Appl., 2000, 241:46-55.
[10] Nakajo K., Takahashi W., Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl., 2003, 279:372-379.
[11] Noor M. A., Some algorithms for general monotone mixed variational inequalities, Math. Comput. Model., 1999, 29:1-9.
[12] Noor M. A., Some development in general variational inequalities, Appl. Math. Comput., 2004, 152:199-277.
[13] Siriyan K., Kangtunyakarn A., A new general system of variational inequalities for convergence theorem and application, Numer Algor., 2019, 81:99-123.
[14] Suzuki T., Strong convergence of Krasnoselskii and Manns type sequences for one parameter nonexpansive semigroups without Bochner integrals, J. Math. Anal. Appl., 2005, 305:227-239.
[15] Sunthrayuth P., Kumam P., Viscosity approximation methods based on generalized contraction mappings for a countable family of strict pseudo-contractions, a general system of variational inequalities and a generalized mixed equilibrium problem in Banach spaces, Math. Comput. Modell., 2013, 58:1814-1828.
[16] Qin X., Cho Y. J., Kang S. M., Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, J. Comput. Appl. Math., 2009, 225:20-30.
[17] Qin X., Lin L. J., Kang S. M., On a generalized Ky Fan inequality and asymptotically strict pseudocontractions in the intermediate sense, J. Optim. Theory. Appl., 2011, 150:553-579.
[18] Qin X., Cho Y. J., Kang S. M., Viscosity approximation methods for generalized equilibrium problems and fixed point problems with applications, Nonlinear Anal., 2010, 72:99-112.
[19] Xu H. K., Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 2004, 298:279-291.
[20] Yao Y., Noor M. A., On viscosity iterative methods for variational inequalities, J. Math. Anal. Appl., 2007, 325:776-787.
[21] Yao Y., Noor M. A., Noor K. I., et al., Modified extragradient methods for a system of variational inequalities in Banach spaces, Acta Appl. Math., 2010, 110:1211-1224.
[22] Zhou H., Convergence theorems of fixed points for k-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal., 2008, 69(2):456-462.
[23] Zhu D. L., Marcotte P., Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities, SIAM J. Optim., 1996, 6:774-726.

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