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On Concave Operators

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Abstract

We prove that a u0–concave operator can include other concave operators, and derive a sufficient and necessary condition for the existence and uniqueness of the fixed point of a kind of u0–concave operator under a weaker condition.

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References

  1. Krasnoselskii, M. A., Zabreiko, P. P.: Geometrical Methods of Nonlinear Analysis, Moscow, 1975 (in Russian)

  2. Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Review, 18, 602–709 (1976)

    Article  MathSciNet  Google Scholar 

  3. Potter, A. J. B.: Applications of Hilbert’s projective metric to certain classes of non-homogenous operators. Quart. J. Math. Oxford Ser., 28(2), 93–99 (1977)

    MATH  MathSciNet  Google Scholar 

  4. Li, F. Y., Liang, Z. D.: Fixed points theorem for φ-concave (convex) operator with applications. J. Sys. Sci.& Math. Scis., 14(4), 335–360 (1994)(in Chinese)

    Google Scholar 

  5. Guo, D. J.: Nonlinear Functional Analysis, Shandong Scientific and Technical Publishers, Ji’nan, 1985 (in Chinese)

  6. Guo, D. J.: Partial Ordering Methods of Nonlinear Functional Analysis, Shandong Scientific and Technical Publishers, Ji’nan, 2000, 3 (in Chinese)

  7. Bushell, P. J.: Hilbert’s metric and positive contraction mappings in a Banach Space. Arch. Rational Mech. Anal., 52, 330–338 (1976)

    MathSciNet  Google Scholar 

  8. Bushell, P. J.: On a Class of Volterea and Fredholm Nonlinear Integral Equations. Math. Proc. Cambridge Philos. Soc., 79, 329–335 (1976)

    MATH  MathSciNet  Google Scholar 

  9. Wan, W. X.: The conditions of contract map and a Banach fixed point theorem. Acta Mathematica Sinica, Chinese Series, 27(1), 35–52 (1984)

    MATH  Google Scholar 

  10. Amann, H.: On the number of nonlinear equations in ordered Banach spaces. J. Funct. Anal., 11, 346–384 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  11. Du, Y. H.: A fixed point theorem for a class of non-compact operators with application. Acta Mathematica Sinica, Chinese Series, 32, 618–627 (1989)

    MATH  Google Scholar 

  12. Guo, D. J.: Fixed points and eigenvalues of a class of concave and convex operator. Chinese Science Bulletin, 30, 1132–1135 (1985) (in Chinese)

    Google Scholar 

  13. Zhao, Z. Q.: Existence and uniqueness of fixed points for mixed monotone mappings in partial ordering space. J. Sys. Sci. & Math. Scis., 19(2), 217–224 (1999)(in Chinese)

    MATH  Google Scholar 

  14. Potter, A. J. B.: Existence theorem for nonlinear integral equation. J. London Math. Soc., 11(2), 7–10 (1975)

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shanxi University, Taiyuan 030006, P. R. China

    Zhan Dong Liang

  2. Department of Mathematics, Zhengzhou University, Zhengzhou 460052, P. R. China

    Zhan Dong Liang

  3. Department of Mathematics, Zhengzhou University, Zhengzhou 460052, P. R. China

    Wen Xia Wang

  4. Department of Mathematics, Taiyuan Teachers College, Taiyuan 030012, P. R. China

    Wen Xia Wang

  5. Department of Mathematics, Shanxi University, Taiyuan 030006, P. R. China

    Sheng Jia Li

Authors
  1. Zhan Dong Liang
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  2. Wen Xia Wang
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  3. Sheng Jia Li
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Correspondence to Zhan Dong Liang.

Additional information

Supported by NSFC (10371068), NSFC(60174007) and Science Foundation of Shanxi Province (20041003)

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Liang, Z.D., Wang, W.X. & Li, S.J. On Concave Operators. Acta Math Sinica 22, 577–582 (2006). https://doi.org/10.1007/s10114-005-0687-1

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  • DOI: https://doi.org/10.1007/s10114-005-0687-1

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