The solutions of a class of operator equations based on different inequality

Volume 9, Issue 2, pp 370--376 http://dx.doi.org/10.22436/jnsa.009.02.03

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Authors

Xiaofang Yan - Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China. Chuanxi Zhu - Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China. Zhaoqi Wu - Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.

Abstract

In this paper, by using random fixed point index theory, some new boundary conditions based on strictly convex or strictly concave functions are established and some new theorems for the solutions of a class of random semi-closed 1-set-contractive operator equations \(A(\omega; x) = \mu x\) are obtained, which extend and generalize some corresponding results of Wang [S. Wang, Fixed Point Theory Appl., 2011 (2011), 7 pages]. Finally, an application to a class of random nonlinear integral equations is given to illustrate the usability of the obtained results.

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Keywords

• Real Banach space
• random semi-closed 1-set-contractive operator
• random topological degree.

MSC

•  47H10
•  60H25

References

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