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

Fengxia Zheng

doi:doi:10.11648/j.ijtam.20170306.12

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

Fengxia Zheng

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 6)

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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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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TY  - JOUR
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

Fengxia Zheng

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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  -

Copy | Download