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New Fixed Point Theorems for Mixed Monotone Operators with Perturbation and Applications

Received: 29 September 2017     Accepted: 23 October 2017     Published: 15 November 2017
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Abstract

By using the properties of cone and the fixed point theorem for mixed monotone operators in ordered Banach spaces, we investigate the mixed monotone operators of a new type with perturbation. We establish some sufficient conditions for such operators to have a new existence and uniqueness fixed point and provide monotone iterative techniques which give sequences convergent to the fixed point. Finally, as applications, we apple the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 6)
DOI 10.11648/j.ijtam.20170306.12
Page(s) 182-190
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Fixed Point, Mixed Monotone Operator, Positive Solution, Fractional Differential Equation, Boundary Value Problem

References
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Cite This Article
  • APA Style

    Fengxia Zheng. (2017). New Fixed Point Theorems for Mixed Monotone Operators with Perturbation and Applications. International Journal of Theoretical and Applied Mathematics, 3(6), 182-190. https://doi.org/10.11648/j.ijtam.20170306.12

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    ACS Style

    Fengxia Zheng. New Fixed Point Theorems for Mixed Monotone Operators with Perturbation and Applications. Int. J. Theor. Appl. Math. 2017, 3(6), 182-190. doi: 10.11648/j.ijtam.20170306.12

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    AMA Style

    Fengxia Zheng. New Fixed Point Theorems for Mixed Monotone Operators with Perturbation and Applications. Int J Theor Appl Math. 2017;3(6):182-190. doi: 10.11648/j.ijtam.20170306.12

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  • @article{10.11648/j.ijtam.20170306.12,
      author = {Fengxia Zheng},
      title = {New Fixed Point Theorems for Mixed Monotone Operators with Perturbation and Applications},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {3},
      number = {6},
      pages = {182-190},
      doi = {10.11648/j.ijtam.20170306.12},
      url = {https://doi.org/10.11648/j.ijtam.20170306.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170306.12},
      abstract = {By using the properties of cone and the fixed point theorem for mixed monotone operators in ordered Banach spaces, we investigate the mixed monotone operators of a new type with perturbation. We establish some sufficient conditions for such operators to have a new existence and uniqueness fixed point and provide monotone iterative techniques which give sequences convergent to the fixed point. Finally, as applications, we apple the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.},
     year = {2017}
    }
    

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    T1  - New Fixed Point Theorems for Mixed Monotone Operators with Perturbation and Applications
    AU  - Fengxia Zheng
    Y1  - 2017/11/15
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ijtam.20170306.12
    DO  - 10.11648/j.ijtam.20170306.12
    T2  - International Journal of Theoretical and Applied Mathematics
    JF  - International Journal of Theoretical and Applied Mathematics
    JO  - International Journal of Theoretical and Applied Mathematics
    SP  - 182
    EP  - 190
    PB  - Science Publishing Group
    SN  - 2575-5080
    UR  - https://doi.org/10.11648/j.ijtam.20170306.12
    AB  - By using the properties of cone and the fixed point theorem for mixed monotone operators in ordered Banach spaces, we investigate the mixed monotone operators of a new type with perturbation. We establish some sufficient conditions for such operators to have a new existence and uniqueness fixed point and provide monotone iterative techniques which give sequences convergent to the fixed point. Finally, as applications, we apple the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.
    VL  - 3
    IS  - 6
    ER  - 

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Author Information
  • Department of Mathematics, Sichuan University of Arts and Science, Dazhou, P. R. China

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