General iterative scheme for finding attractive points of （α，β）—mildly hybrid set—valued mappings in Banach spaces

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）