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        賦Luxemburg范數(shù)的Orlicz空間的M-常數(shù)

        2022-05-30 20:32:49王梓萱崔云安王靜

        王梓萱 崔云安 王靜

        摘要:Riesz角度μ2(x)是Banach格空間中一個重要的幾何常數(shù),其與空間的不動點性質(zhì)密切相關(guān)。研究了賦Luxemburg范數(shù)的Orlicz序列空間的M-常數(shù)和賦Luxemburg范數(shù)的Orlicz函數(shù)空間的M-常數(shù),并在此基礎(chǔ)上還給出了EΦ具有弱不動點性質(zhì)的判別準(zhǔn)則。

        關(guān)鍵詞:M-常數(shù);Orlicz空間;Luexmburg范數(shù);Riesz角度

        DOI:10.15938/j.jhust.2022.04.018

        中圖分類號: O177.2

        文獻(xiàn)標(biāo)志碼: A

        文章編號: 1007-2683(2022)04-0142-05

        M-constants in Orlicz Spaces Equipped

        with the Luxemburg Norm

        WANG Zi-xuan,CUI Yun-an,WANG Jing

        (School of Science, Harbin University of Science and Technology, Harbin 150080,China)

        Abstract:Riesz angle μ2(x) is an important geometric constant in Banach lattice spaces, which is closely related to the fixed point properties of spaces.?In this paper, the M-constants of Orlicz function spaces and Orlicz sequence spaces equipped with Luxemburg norm are obtained.?On this basis, a criteria for EΦhas weak fixed point property was also given.

        Keywords:M-constants; Orlicz spaces; Luxemburg norm; Riesz angles

        0引言

        1預(yù)備知識

        2Orlicz序列空間的M-常數(shù)

        3Orlicz函數(shù)空間的M-常數(shù)

        參 考 文 獻(xiàn):

        [1]SIMS B. Orthogonality and Fixed Points of Nonexpansive Maps[J]. Proc. Cent. Anal. Nat. Univ, 1988, 20: 178.

        [2]CUI YA, FORALEWSKI P, HUDZIK H. M-constants in Orlicz-Lorentz Function Spaces[J]. Mathematische Nachrichten, 2019, 292(12): 2556.

        [3]CUI YA, FORALEWSKI, PAWEL, et al. M-constants in Orlicz-Lorntz Sequence Spaces with Applications to Fixed Point Theory[J]. Fixed Point Theory An International Journal, 2018, 19(1): 141.

        [4]HE X, CUI YA, HUDZIK H. The Fixed Point Property of Orlicz Sequence Spaces Equipped with the P-Amemiya Norm[J]. Fixed Point Theory and Applications, 2013(1):1.

        [5]CUI YA, HUDZIK H, WISIA M. M-Constants, Dominguez-Benavides Coefficient, and Weak Fixed Point Property in Orlicz Sequence Spaces Equipped with the P-Amemiya Norm[J]. Fixed Point Theory and Applications, 2016, 89: 1.

        [6]ABRAMOVICH Y. A., LOZANOVSKI G. Y. Certain Numerical Characteristics of KN-lineals[J]. Mathematical Notes, 1973, 14(5): 973.

        [7]LIFSHITS E. A. On the Theory of Partially Ordered Banach Spaces[J]. Functional Analysis and Its Applications, 1969, 4(1): 75.

        [8]LUXEMBURG W. Banach Function Spaces[J]. Van Gorcum, 1955, 129: 1.

        [9]KRASNOSEL′SKI, M. A, RUTICKI, JA. B. Convex Functions and Orlicz Spaces[J]. P. Noordhoff, 1961.

        [10]KRASNOSELSKI. M. A. Convex Functions and Orlicz Spaces[J]. US Atomic Energy Commission, 1960: 80.

        [11]YAN Y. Riesz Angles of Orlicz Sequence Spaces[J]. Commentationes Mathematicae Universitatis Carolinae, 2002, 43(1): 938.

        [12]孟院花. Banach格的直和性質(zhì)[D]. 成都:西南交通大學(xué), 2016:1.

        [13]崔云安,郭晶晶.與不動點性質(zhì)相關(guān)的新常數(shù)[J].哈爾濱理工大學(xué)學(xué)報, 2016, 21(2): 122.CUI Yunan, GUO Jingjing. A New Constant Associated with the Fixed Point Property[J]. Journal of Harbin University of Science and Technology , 2016, 21(2): 122.

        [14]王稀. Banach空間中與不動點性質(zhì)有關(guān)的幾何性質(zhì)[D].哈爾濱:哈爾濱工業(yè)大學(xué),2017.

        (編輯:溫澤宇)

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