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渐近正则映射对的不动点

B. K. 沙玛 B. S. 撒克

B. K. 沙玛, B. S. 撒克. 渐近正则映射对的不动点[J]. 应用数学和力学, 1997, 18(8): 717-724.
引用本文: B. K. 沙玛, B. S. 撒克. 渐近正则映射对的不动点[J]. 应用数学和力学, 1997, 18(8): 717-724.
B. K. Sharma, B. S. Thakur. Fixed Points of a Pair of Asymptotically Regular Mappings[J]. Applied Mathematics and Mechanics, 1997, 18(8): 717-724.
Citation: B. K. Sharma, B. S. Thakur. Fixed Points of a Pair of Asymptotically Regular Mappings[J]. Applied Mathematics and Mechanics, 1997, 18(8): 717-724.

渐近正则映射对的不动点

Fixed Points of a Pair of Asymptotically Regular Mappings

  • 摘要: 本文在P一致凸Banach空间中证明了浙近正则映射对的若干不动点定理.在Hilbert空间,Lp空间,Hardy空间Hp和Sobolev空间Hp,k中,1[9,10],Kruppel[11,12]和其他作者的结果.
  • [1] J. Barros-Neto An Introduction to the Theory of Distribution Dekker,New York (1973).
    [2] F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functionalequations in Banach spaces, Bull. Amer. Math. Soc., 72 (1966), 671~675.
    [3] W. L. Bynum. Normal structure coefficients for Banach spaces, Pacthe J. Math.. 86(1980). 427~436.
    [4] E. Casini and E. Maluta. Fixed points of uniformly Lipschitzian mappings in spaces withuniformly normal structure. Nonlinear.Anal., 9 (1985), 103~108.
    [5] J. Danes.On densifying and related mappings and their applications in nonlinearfunctional analysis, Theory of Nonlinear Operators. Proc. Suminer School, Oct. 1972,GDR. Akademie-Verlag. Berlin (1974), 15~56.
    [6] N. Dunford and J. Schwarz. Linear Operators. Vol.1. Interscience, New York (1958).
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    [8] K. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge Stud. Ady.Math., 28. Cambridge Univ. Press. London (1990).
    [9] J. Gornicki, Fixed point theorems for asymptotically regular mappings in Lp spaces. Non.linear Anal, 17 (1991), 153~159.
    [10] J. Gornicki. Fixed points of asymptotically regular mappings. Math. Slovaca. 43, 3(1993), 327~336.
    [11] M. Kruppel, Ein Fixpunktsatz fur asymptotisch regulare operatoren im Hilbert-Raum.Wiss. Z. Padagog. Hochsch. Liselotte Herrman Gustrow, Math.Natur. Fak., 25(1987), 241~246.
    [12] M. Kruppel, Ein Fixpunktsatz fur asymptotisch regulare Operatoren im gleichmdfgkonvexen Banach-Raum, Wiss. Z. Padagog. Hochsch. "Liselotte Herman" Gustrow,Math.Natur. Fak., 27 (1989), 247~251.
    [13] T. C. Lim, H. K. Xu and Z. B. Xu, An Lp inequalities and its applications to tixed pointtheory and approximation theory, Progress in Approximation Theory, Academic Press(1991), 609~624.
    [14] P. K. Lin, A uniformly asymptotically regular mappings without fixed points, Canad.Math. Bull., 30 (1987), 481~483.
    [15] J. Lindenstrauss and L. Tzafriri, Chasical Banach Spaces, Ⅱ-Function Spaces,Springer-Verlag, New York, Berlin (1979).
    [16] S. A. Pichugov. Jung's constant of the space Lp,(in Russian), Mat. Zametki, 43 (1988),604~614. (Translation: Math. Notes, 43 (1988), 348~354.)
    [17] B. Prus and R. Smarzewski, Strongly unique best approximations and centers inuniformly convex spaces, J. Math. Anal. Appl., 121 (1987), 10~21.
    [18] S. Prus-on Bynum's fixed point theorem, Atti Sem. Mat. Fis. Unliv. Modena, 38 (1990),535~545.
    [19] S. Prus, Some estimates for the normal structure coefficient in Banach spaces, RendCirc. Mat. Palermo, 40, 2 (1991),128~135.
    [20] R. Smarzewski Strongly unique best approximations in Banach spaces Ⅱ, J. Approx.Theory, 51 (1987), 202~217.
    [21] R. Smarzewski, On the inequality of Bynum and Drew, J. Math. Anal. Appl., 150 (1990),146~150.
    [22] H. K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal., 16 (1991)1127~1138.
    [23] C. Zalinescu, On uniformly convex function, J. Math. Anal. Appl., 95 (1983), 344~374.
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出版历程
  • 收稿日期:  1996-11-20
  • 刊出日期:  1997-08-15

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