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T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Analysis. 65 (2006), 1379-1393.

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Article

A Note on the Unique Solution of the Integral Equations in the Framework of Fixed Point Theorem on Partially Ordered Metric Space

1College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, China


American Journal of Applied Mathematics and Statistics. 2016, Vol. 4 No. 5, 154-160
DOI: 10.12691/ajams-4-5-3
Copyright © 2016 Science and Education Publishing

Cite this paper:
Youhua Qian, Juan Wu, Yafei Zhang. A Note on the Unique Solution of the Integral Equations in the Framework of Fixed Point Theorem on Partially Ordered Metric Space. American Journal of Applied Mathematics and Statistics. 2016; 4(5):154-160. doi: 10.12691/ajams-4-5-3.

Correspondence to: Youhua  Qian, College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, China. Email: qyh2004@zjnu.edu.cn

Abstract

In this paper, we obtained the unique solution of the integral and coupled integral equation in the framework of fixed point theorem on partially ordered metric space. Our results unified some methods in studying the existence of unique solution for the integral equation. Moreover, all results are much more brief. In addition, the examples are given to illustrate the usability of the obtained results.

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