On the Existence of Solutions of Some Stochastic Functional Integral Equations

• Autorzy: Pasławska-Południak M.
• Języki publikacji: EN

Abstrakty

EN

The integral equation of Urysohn type is considered, for the deterministic and stochastic cases . We show, using the fixed point theorem of Darbo type that under some assumptions the equations have solutions belonging to the space of continuous functions. The main tool used in our paper is the technique associated with measures of noncompactness.

Słowa kluczowe

EN

measures of noncompactness; functional integral equations; stochastic functional integral equations

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2010
• Tom: Vol. 50, [Z] 1
• Strony: 49--60
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Pasławska-Południak M.

• Department of Mathematics, Rzeszów University of Technology W. Pola 2, 35-959 Rzeszów, Poland,

Bibliografia

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• [3] J. Banaś and M. Pasławska-Południak, Monotonic solutions of Urysohn integral equation on unbounded interval, Int. J. Comput. Math. Appl., 47 (2004), 1947-1954.
• [4] J. Banaś, D. Szynal and S. Wedrychowicz, On existence, asymptotic behavior and stability of solutions of stochastic integral equations, Stoch. Annal. Appl., 9, (4) (1991), 363-385.
• [5] R. Liptser and A. Shiryayev, Statistics of Random Processes, Springer, Berlin, 1977.
• [6] D. Szynal and S. Wedrychowicz, On existence and asymptotic behavior of solutions of a nonlinear stochastic integral equation, Ann. Mat. Pura Appl., 142, (4) (1985), 105-119.
• [7] D. Szynal and S. Wedrychowicz, On existence and asymptotic behavior of random solutions of a class of stochastic functional - integral equations, Coll. Mat, 51 (1987), 349-364.
• [8] D. Szynal and S. Wedrychowicz, On solutions of a stochastic integral equations of the Volterra - Fredholm type, Ann. Univ. Mariae Curie - Skłodowska, Sectio A, 53, (2) (1989), 107-122.