Wang Qianwen　Wei Qiuhong　Zeng Liuchuan

Abstract： In this paper，we first introduce the concepts of （α，β）-mildly hybrid set-valued mappings and condition I*，and then propose a general iterative method for finding attractive points of （α，β） -mildly hybrid set-valued mappings.Moreover，we establish strong convergence of the proposed iterative scheme for （α，β）-mildly hybrid set-valued mappings in a uniformly convex Banach space by using condition I* and demi-compact property.Our results improve and modify the corresponding ones announced by other authors in the literature.

Key words： mildly hybrid set-valued mapping； condition I*； strongly attractive point； attractive point； uniformly convex Banach space

CLC number： O 177.91 Document code： A Article ID： 1000-5137（2018）04-0397-09

摘 要： 引入（α，β）-適度混合集值映像與條件I*的概念，提出了用于尋求（α，β）-適度混合集值映像吸引點(diǎn)的一般迭代法.在一致凸Banach空間中，利用條件I*與半緊性質(zhì)，建立了所提（α，β）-適度混合集值映像的迭代格式的強(qiáng)收斂性.結(jié)論改進(jìn)與修正了之前文獻(xiàn)中已發(fā)布的相應(yīng)結(jié)果.

關(guān)鍵詞： 適度混合集值映像； 條件I*； 強(qiáng)吸引點(diǎn)； 吸引點(diǎn)； 一致凸Banach空間

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（責(zé)任編輯：馮珍珍）