Application of random fixed point theorems in solving nonlinear stochastic integral equation of the Hammerstein type
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DOI:
https://doi.org/10.26637/mjm102/007Abstract
In the present paper, we apply random analogue Kannan fixed point theorem [10] to analyze the existence of a solution of a nonlinear stochastic integral equation of the Hammerstein type of the form
$$
x(t ; \omega)=h(t ; \omega)+\int_S k(t, s ; \omega) f(s, x(s ; \omega)) d \mu(s)
$$
where \(t \in S\), a \(\sigma\)-finite measure space with certain properties, \(\omega \in \Omega\), the supporting set of a probability measure space \((\Omega, \beta, \mu)\) and the integral is a Bochner integral.
Keywords:
Random fixed point, Kannan operator, stochastic integral equationMathematics Subject Classification:
47H10, 60H25- Pages: 54-59
- Date Published: 01-04-2013
- Vol. 1 No. 02 (2013): Malaya Journal of Matematik (MJM)
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