New Fixed Point Theorems for Mixed Monotone Operators with Perturbation and Applications
International Journal of Theoretical and Applied Mathematics
Volume 3, Issue 6, December 2017, Pages: 182-190
Received: Sep. 29, 2017; Accepted: Oct. 23, 2017; Published: Nov. 15, 2017
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Author
Fengxia Zheng, Department of Mathematics, Sichuan University of Arts and Science, Dazhou, P. R. China
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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.
Keywords
Fixed Point, Mixed Monotone Operator, Positive Solution, Fractional Differential Equation, Boundary Value Problem
To cite this article
Fengxia Zheng, New Fixed Point Theorems for Mixed Monotone Operators with Perturbation and Applications, International Journal of Theoretical and Applied Mathematics. Vol. 3, No. 6, 2017, pp. 182-190. doi: 10.11648/j.ijtam.20170306.12
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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