發(fā)布時(shí)間：2019-03-02 14:24

【摘要】：本文主要考慮了依中間意義漸近擬φ非擴(kuò)張映像和含松弛η-α-單調(diào)映像的混合平衡問(wèn)題的強(qiáng)收斂性問(wèn)題,運(yùn)用混合方法,將結(jié)果本質(zhì)地推廣和改進(jìn)近來(lái)許多已有的相應(yīng)結(jié)果.具體闡述如下：在第一章中,主要討論了與課題相關(guān)的國(guó)內(nèi)外學(xué)者研究的熱點(diǎn)問(wèn)題,近幾年來(lái)已有的一些學(xué)者的研究成果,以及文章的背景和優(yōu)勢(shì)以突現(xiàn)本課題的應(yīng)用價(jià)值和實(shí)際意義.在第二章中,主要給出了一些與本文相關(guān)的預(yù)備知識(shí),概念以及符號(hào).在第三章中,主要研究了一般空間中兩類問(wèn)題的第一種迭代逼近解的收斂性,通過(guò)構(gòu)造第一種新的迭代算法,證明了在一定條件下,算法所生成的迭代序列強(qiáng)收斂到無(wú)限簇依中間意義漸近擬φ非擴(kuò)張映像和含松弛η-α-單調(diào)映像的混合平衡問(wèn)題的公共元.主要從漸近擬φ非擴(kuò)張映像推廣到依中間意義漸近擬φ非擴(kuò)張映像,從廣義混合平衡問(wèn)題推廣到含松弛η-α-單調(diào)映像的混合平衡問(wèn)題,改進(jìn)了2012年Yang L等的主要結(jié)果；從一致凸和一致光滑的Banach空間推廣到一致光滑、嚴(yán)格凸且具有Kadec-Klee性質(zhì)的Banach空間,從擬φ非擴(kuò)張映像推廣到依中間意義漸近擬φ非擴(kuò)張映像,從廣義平衡問(wèn)題推廣到含松弛η-α-單調(diào)映像的混合平衡問(wèn)題,改進(jìn)了2013年孔德州的主要結(jié)果.同時(shí),結(jié)果還改進(jìn)和推廣了近來(lái)其它相關(guān)文獻(xiàn)中的結(jié)果,詳見第三章.在第四章中,主要研究了一般空間中兩類問(wèn)題的第二種迭代逼近解的收斂性,通過(guò)構(gòu)造第二種新的迭代算法,證明了在一定條件下,算法所生成的迭代序列強(qiáng)收斂到無(wú)限簇依中間意義漸近擬φ非擴(kuò)張映像和無(wú)限簇含松弛η-α-單調(diào)映像的混合平衡問(wèn)題的公共元.主要從一致凸和一致光滑的Banach空間推廣到一致光滑、嚴(yán)格凸且具有Kadec-Klee性質(zhì)的Banach空間,從擬φ非擴(kuò)張映像推廣到依中間意義漸近擬φ非擴(kuò)張映像,從一個(gè)含松弛η-α-單調(diào)映像的混合平衡問(wèn)題推廣到一簇含松弛η-α-單調(diào)映像的混合平衡問(wèn)題,改進(jìn)了2014年Chen M.J.等的主要結(jié)果；從一個(gè)平衡問(wèn)題推廣到一簇含松弛η-α-單調(diào)映像的混合平衡問(wèn)題,改進(jìn)了2014年Huang C.Y.等的主要結(jié)果.同時(shí),結(jié)果還改進(jìn)和推廣了近來(lái)相其它關(guān)文獻(xiàn)中的結(jié)果,詳見第四章.
[Abstract]:In this paper, we mainly consider the strong convergence of mixed equilibrium problems for asymptotically quasi-蠁 nonexpansive mappings and relaxed 畏-偽-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-偽-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-偽-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-偽-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-偽-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-偽-monotone mappings to a family of mixed equilibrium problems with relaxed 畏-偽-monotone mappings, the Chen M.J. 2014 is improved. From an equilibrium problem to a cluster of mixed equilibrium problems with relaxed 畏-偽-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.
【學(xué)位授予單位】：浙江師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O177.91

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本文編號(hào)：2433132