Existence of Solutions of Nonlinear Stochastic Volterra Fredholm Integral Equations of Mixed Type

We establish sufficient conditions for the existence and uniqueness of random solutions of nonlinear Volterra-Fredholm stochastic integral equations of mixed type by using admissibility theory and fixed point theorems. The results obtained in this paper generalize the results of several papers.

[1]  A. T. Bharucha-Reid,et al.  Random Integral Equations , 2012 .

[2]  Chris P. Tsokos,et al.  Existence and stability behavior of random solutions of a system of nonlinear random equations , 1975, Inf. Sci..

[3]  S. T. Hardiman,et al.  On the Uryson type of stochastic integral equations , 1974, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  V. Rao.  On random solutions of Volterra-Fredholm integral equations , 1983 .

[5]  D. Szynal,et al.  ON SOLUTIONS OF SOME NONLINEAR STOCHASTIC INTEGRAL EQUATIONS , 1993 .

[6]  A stochastic system for communicable diseases , 1974 .

[7]  W. J. Padgett,et al.  On a Stochastic Integro-Differential Equation of Volterra Type , 1972 .

[8]  Random contractors with random nonlinear majorant functions , 1979 .

[9]  On existence,asymptotic behaviour and stability of solutions of stochastic integral equations , 1991 .

[10]  K. Balachandran,et al.  Existence of solutions of a class of stochastic Volterra integral equations with applications to chemotherapy , 1999, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[11]  S. T. Hardiman,et al.  A stochastic model for metabolizing systems with computer simulation , 1973 .

[12]  On a Class of Nonlinear Stochastic Integral Equations , 1974 .

[13]  K. Balachandran,et al.  Existence of Solutions of General Nonlinear Stochastic Volterra Fredholm Integral Equations , 2005 .

[14]  W. J. Padgett,et al.  Solution of a Stochastic Integral Equation Using Integral Contractors , 1979, Inf. Control..

[15]  Solution of random operator equations by random step-contractors☆ , 1980 .

[16]  Existence and stability behaviour of a non-linear perturbed stochastic system , 1974 .

[17]  D. Szynal,et al.  On solutions of a stochastic integral equation of the volterra type with applications for chemotherapy , 1988, Journal of Applied Probability.

[18]  On random solutions of Fredholm integral equations , 1960 .

[19]  W. J. Padgett,et al.  Random contractors and the solution of random nonlinear equations , 1977 .

[20]  W. J. Padgett,et al.  On random nonlinear contractions , 1977, Mathematical systems theory.

[21]  W. J. Padgett,et al.  On a random Volterra integral equation , 1973, Mathematical systems theory.

[22]  W. J. Padgett,et al.  On a Class of Stochastic Integral Equations of Mixed Type , 1977, Inf. Control..

[23]  S. T. Hardiman,et al.  Existence theorems for non-linear random integral equations with time lags , 1976 .

[24]  K. Balachandran,et al.  Existence of Random Solutions of a General Class of Stochastic Functional Integral Equations , 2003 .

[25]  W. J. Padgett,et al.  Random integral equations with applications to stochastic systems , 1971 .

[26]  D. Szynal,et al.  On existence and asymptotic behaviour of solutions of a nonlinear stochastic integral equation , 1985 .

[27]  Chris P. Tsokos,et al.  Random integral equations with applications to life sciences and engineering , 1974 .

[28]  A. T. Bharucha-Reid.  Approximate solution of random equations , 1979 .

[29]  Existence of a Solution of a Stochastic Integral Equation in Turbulence Theory , 1971 .

[30]  W. J. Padgett,et al.  Almost surely continuous solutions of a nonlinear stochastic integral equation , 1976, Mathematical systems theory.

[31]  A random Fredholm integral equation , 1972 .

[32]  W. J. Padgett,et al.  A new stochastic formulation of a population growth problem , 1973 .

[33]  W. J. Padgett.  On non-linear perturbations of stochastic Volterra integral equations , 1973 .

[34]  W. J. Padgett,et al.  Random solution of a stochastic integral equation :almost sure and mean square convergence of successive approximations , 1973 .

[35]  C. Tsokos,et al.  Existence and boundedness of random solutions to stochastic functional integral equations , 1977 .

[36]  C. Tsokos,et al.  On a random solution of a nonlinear perturbed stochastic integral equation of the Volterra type , 1973, Bulletin of the Australian Mathematical Society.

[37]  Chris P. Tsokos,et al.  On a stochastic integral equation of the Volterra type , 1969, Journal of Applied Probability.

[38]  C. Tsokos,et al.  On a nonlinear stochastic integral equation with application to control systems , 1976 .

[39]  W. J. Padgett,et al.  On a semi-stochastic model arising in a biological system , 1970 .

[40]  C. Tsokos,et al.  On the existence of random solutions of a non-linear perturbed random integral equation , 1978 .

[41]  C. Tsokos,et al.  On the existence of a random solution to a nonlinear perturbed stochastic integral equation , 1976 .

[42]  Chris P. Tsokos,et al.  On the Existence, Uniqueness, and Stability Behavior of a Random Solution to a Nonlinear Perturbed Stochastic Integro-Differential Equation , 1975, Inf. Control..

[43]  W. J. Padgett,et al.  On a stochastic integral equation of the fredholm type , 1972 .

[44]  H. Onose.  On the Boundedness of Random Solutions of Nonlinear Stochastic Integral Equations , 1986 .

[45]  Louis B. Rall,et al.  Nonlinear Functional Analysis and Applications , 1971 .

[46]  Uniwersytet Marii Curie-Skłodowskiej w Lublinie,et al.  Annales Universitatis Mariae Curie-Skłodowska , 2001 .