Abstract
In this paper, we prove some random fixed point theorems in generalized Banach spaces. We establish a random version of a Krasnoselskii-type fixed point theorem for the sum of a contraction random operator and a compact operator. The results are used to prove the existence of solution for random differential equations with initial and boundary conditions. Finally, some examples are given to illustrate the results.
Funding source: Ministerio de Economía y Competitividad (Spain)
Award Identifier / Grant number: MTM2010-15314
Funding source: European Commission
Award Identifier / Grant number: FEDER
Funding statement: The research has partially been supported by Ministerio de Economía y Competitividad (Spain), project MTM2010-15314, and co-financed by the European Community fund FEDER.
This paper was completed while M. L. Sinacer and A. Ouahab visited the Department of MÁthematical AnÁlysis of the University of Santiago de Compostela. They would like to thank the department for its hospitality and support.
References
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Some comments on infinities on quantum field theory: A functional integral approach
- Random fixed point theorem in generalized Banach space and applications
- Exponential stability for stochastic neutral functional differential equations driven by Rosenblatt process with delay and Poisson jumps
- Numerical study of stochastic Volterra–Fredholm integral equations by using second kind Chebyshev wavelets
- Limit behavior of the Esscher premium
Articles in the same Issue
- Frontmatter
- Some comments on infinities on quantum field theory: A functional integral approach
- Random fixed point theorem in generalized Banach space and applications
- Exponential stability for stochastic neutral functional differential equations driven by Rosenblatt process with delay and Poisson jumps
- Numerical study of stochastic Volterra–Fredholm integral equations by using second kind Chebyshev wavelets
- Limit behavior of the Esscher premium