一般空间中两类问题的迭代逼近解的收敛性之研究
发布时间：2019-03-02 14:24
【摘要】：本文主要考虑了依中间意义渐近拟φ非扩张映像和含松弛η-α-单调映像的混合平衡问题的强收敛性问题,运用混合方法,将结果本质地推广和改进近来许多已有的相应结果.具体阐述如下：在第一章中,主要讨论了与课题相关的国内外学者研究的热点问题,近几年来已有的一些学者的研究成果,以及文章的背景和优势以突现本课题的应用价值和实际意义.在第二章中,主要给出了一些与本文相关的预备知识,概念以及符号.在第三章中,主要研究了一般空间中两类问题的第一种迭代逼近解的收敛性,通过构造第一种新的迭代算法,证明了在一定条件下,算法所生成的迭代序列强收敛到无限簇依中间意义渐近拟φ非扩张映像和含松弛η-α-单调映像的混合平衡问题的公共元.主要从渐近拟φ非扩张映像推广到依中间意义渐近拟φ非扩张映像,从广义混合平衡问题推广到含松弛η-α-单调映像的混合平衡问题,改进了2012年Yang L等的主要结果；从一致凸和一致光滑的Banach空间推广到一致光滑、严格凸且具有Kadec-Klee性质的Banach空间,从拟φ非扩张映像推广到依中间意义渐近拟φ非扩张映像,从广义平衡问题推广到含松弛η-α-单调映像的混合平衡问题,改进了2013年孔德州的主要结果.同时,结果还改进和推广了近来其它相关文献中的结果,详见第三章.在第四章中,主要研究了一般空间中两类问题的第二种迭代逼近解的收敛性,通过构造第二种新的迭代算法,证明了在一定条件下,算法所生成的迭代序列强收敛到无限簇依中间意义渐近拟φ非扩张映像和无限簇含松弛η-α-单调映像的混合平衡问题的公共元.主要从一致凸和一致光滑的Banach空间推广到一致光滑、严格凸且具有Kadec-Klee性质的Banach空间,从拟φ非扩张映像推广到依中间意义渐近拟φ非扩张映像,从一个含松弛η-α-单调映像的混合平衡问题推广到一簇含松弛η-α-单调映像的混合平衡问题,改进了2014年Chen M.J.等的主要结果；从一个平衡问题推广到一簇含松弛η-α-单调映像的混合平衡问题,改进了2014年Huang C.Y.等的主要结果.同时,结果还改进和推广了近来相其它关文献中的结果,详见第四章.
[Abstract]:In this paper, we mainly consider the strong convergence of mixed equilibrium problems for asymptotically quasi-蠁 nonexpansive mappings and relaxed 畏-伪-monotone mappings in the intermediate sense. The results essentially generalize and improve many recent corresponding results. The main contents are as follows: in the first chapter, the author mainly discusses the hot issues of domestic and foreign scholars concerned with the subject, and the research results of some scholars in recent years. And the background and advantages of the article to highlight the application value and practical significance of this topic. In the second chapter, some preparatory knowledge, concepts and symbols related to this paper are given. In the third chapter, we mainly study the convergence of the first iterative approximation solution of the two kinds of problems in general space. By constructing the first iterative algorithm, we prove that under certain conditions, the convergence of the first iterative approximation solution of the two kinds of problems in general space is proved. The iterative sequence generated by the algorithm converges strongly to the common element of the mixed equilibrium problem for asymptotically quasi-蠁 nonexpansive mappings and relaxed 畏-伪-monotone mappings in an infinite cluster according to the intermediate meaning. It is mainly extended from asymptotically quasi-蠁 nonexpansive mapping to asymptotically quasi-蠁 nonexpansive mapping according to the intermediate meaning, from generalized mixed equilibrium problem to mixed equilibrium problem with relaxed 畏-伪-monotone mapping, which improves the main results of Yang L et al in 2012. From uniformly convex and uniformly smooth Banach spaces to uniformly smooth, strictly convex Banach spaces with Kadec-Klee property, and from quasi 蠁 nonexpansive mappings to asymptotically quasi 蠁 nonexpansive mappings in intermediate sense, The generalized equilibrium problem is extended to the mixed equilibrium problem with relaxation 畏-伪-monotone mapping, and the main results of Kongduan in 2013 are improved. At the same time, the results also improve and generalize the results in other related literature, see chapter 3 in detail. In the fourth chapter, we mainly study the convergence of the second iterative approximation solution of the two kinds of problems in general space. By constructing the second iterative algorithm, we prove that under certain conditions, the convergence of the second iterative approximation solution of the two kinds of problems in general space is proved. The iterative sequence generated by the algorithm converges strongly to the common elements of the mixed equilibrium problem of infinite clusters with asymptotically quasi-蠁 nonexpansive mappings and infinite clusters containing relaxed 畏-伪-monotone mappings in the intermediate sense. From uniformly convex and uniformly smooth Banach spaces to uniformly smooth, strictly convex Banach spaces with Kadec-Klee property, and from quasi 蠁 nonexpansive mappings to asymptotically quasi 蠁 nonexpansive mappings in intermediate sense, From a mixed equilibrium problem with relaxed 畏-伪-monotone mappings to a family of mixed equilibrium problems with relaxed 畏-伪-monotone mappings, the Chen M.J. 2014 is improved. From an equilibrium problem to a cluster of mixed equilibrium problems with relaxed 畏-伪-monotone mappings, the Huang C.Y. 2014 is improved. And so on. At the same time, the results also improve and generalize the results in other recent literature, see chapter 4 in detail.
【学位授予单位】：浙江师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O177.91
本文编号：2433132
[Abstract]:In this paper, we mainly consider the strong convergence of mixed equilibrium problems for asymptotically quasi-蠁 nonexpansive mappings and relaxed 畏-伪-monotone mappings in the intermediate sense. The results essentially generalize and improve many recent corresponding results. The main contents are as follows: in the first chapter, the author mainly discusses the hot issues of domestic and foreign scholars concerned with the subject, and the research results of some scholars in recent years. And the background and advantages of the article to highlight the application value and practical significance of this topic. In the second chapter, some preparatory knowledge, concepts and symbols related to this paper are given. In the third chapter, we mainly study the convergence of the first iterative approximation solution of the two kinds of problems in general space. By constructing the first iterative algorithm, we prove that under certain conditions, the convergence of the first iterative approximation solution of the two kinds of problems in general space is proved. The iterative sequence generated by the algorithm converges strongly to the common element of the mixed equilibrium problem for asymptotically quasi-蠁 nonexpansive mappings and relaxed 畏-伪-monotone mappings in an infinite cluster according to the intermediate meaning. It is mainly extended from asymptotically quasi-蠁 nonexpansive mapping to asymptotically quasi-蠁 nonexpansive mapping according to the intermediate meaning, from generalized mixed equilibrium problem to mixed equilibrium problem with relaxed 畏-伪-monotone mapping, which improves the main results of Yang L et al in 2012. From uniformly convex and uniformly smooth Banach spaces to uniformly smooth, strictly convex Banach spaces with Kadec-Klee property, and from quasi 蠁 nonexpansive mappings to asymptotically quasi 蠁 nonexpansive mappings in intermediate sense, The generalized equilibrium problem is extended to the mixed equilibrium problem with relaxation 畏-伪-monotone mapping, and the main results of Kongduan in 2013 are improved. At the same time, the results also improve and generalize the results in other related literature, see chapter 3 in detail. In the fourth chapter, we mainly study the convergence of the second iterative approximation solution of the two kinds of problems in general space. By constructing the second iterative algorithm, we prove that under certain conditions, the convergence of the second iterative approximation solution of the two kinds of problems in general space is proved. The iterative sequence generated by the algorithm converges strongly to the common elements of the mixed equilibrium problem of infinite clusters with asymptotically quasi-蠁 nonexpansive mappings and infinite clusters containing relaxed 畏-伪-monotone mappings in the intermediate sense. From uniformly convex and uniformly smooth Banach spaces to uniformly smooth, strictly convex Banach spaces with Kadec-Klee property, and from quasi 蠁 nonexpansive mappings to asymptotically quasi 蠁 nonexpansive mappings in intermediate sense, From a mixed equilibrium problem with relaxed 畏-伪-monotone mappings to a family of mixed equilibrium problems with relaxed 畏-伪-monotone mappings, the Chen M.J. 2014 is improved. From an equilibrium problem to a cluster of mixed equilibrium problems with relaxed 畏-伪-monotone mappings, the Huang C.Y. 2014 is improved. And so on. At the same time, the results also improve and generalize the results in other recent literature, see chapter 4 in detail.
【学位授予单位】：浙江师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O177.91
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