(α,β)－廣義混合集值映射的吸收點(diǎn)和收斂性定理

陳麗麗　鄒潔　高璐

摘 要：集值映射理論在控制論、優(yōu)化理論、數(shù)理經(jīng)濟(jì)等諸多領(lǐng)域都有著廣泛的應(yīng)用，現(xiàn)已成為非線性分析的重要組成部分，因此研究集值映射的有關(guān)問(wèn)題具有重要的理論意義和應(yīng)用價(jià)值。主要研究了一致凸的Banach空間上（α，β）-廣義混合集值映射吸收點(diǎn)的收斂性問(wèn)題，引入了集值映射意義下的Agarwal迭代格式， 并分別利用I′條件和半緊性質(zhì)給出了一致凸的Banach空間上（α，β）-廣義混合集值映射在該迭代格式下關(guān)于吸收點(diǎn)的收斂性定理。

關(guān)鍵詞：Agarwal迭代格式;（α，β）-廣義混合集值映射;吸收點(diǎn);一致凸Bananch空間

DOI：10.15938/j.jhust.2019.03.023

中圖分類號(hào)： O177.2

文獻(xiàn)標(biāo)志碼： A

文章編號(hào)： 1007-2683（2019）03-0138-05

Abstract：Setvalued mapping theory，which is widely used in control theory， optimization theory， mathematical economics and other fields，has developed rapidly in recent decades and has now become an important component of nonlinear analysis. Therefore， research on related problems of set value mappings has an important theoretical significance and application value. We mainly discuss the convergence problems of attractive points of （α，β）-generalized hybrid setvalued mappings， and we also generalize the Agarwal iteration to the case of setvalued mappings. Consequently， some convergence theorems of attractive points of （α，β）-generalized hybrid setvalued mappings defined on uniformly convex Banach spaces by use of the conditions I′ and the demicompact property are obtained respectively.

Keywords：Agarwal iteration; （α，β）-generalized hybrid setvalued mapping; attractive point; uniformly convex Banach space

3 結(jié) 論

本文主要研究了（α，β）-廣義混合集值映射在Agarwal迭代格式下的吸收點(diǎn)和收斂性問(wèn)題， 事實(shí)上，Agarwal迭代速度在某些條件下比引言中2015年Y.C.Zheng給出的迭代格式收斂速度更快。 我們分別利用I′條件和半緊性質(zhì)給出了一致凸Banach空間上（α，β）-廣義混合集值映射的收斂定理，在此基礎(chǔ)上可以繼續(xù)研究（α，β）-廣義混合集值映射及其它類型的廣義集值映射的吸收點(diǎn)和收斂性問(wèn)題。

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（編輯：關(guān) 毅）