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Abstract
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.
Highlights
Random or stochastic integral equations are important in the study of many physical phenomena in life sciences, engineering, and technology 1–13
Many papers have been appeared on the problem of existence of solutions of nonlinear random integral equations and the results are established by applying various fixed point techniques
In this paper we will study the existence of random solutions of nonlinear stochastic integral equations of mixed type
Summary
Random or stochastic integral equations are important in the study of many physical phenomena in life sciences, engineering, and technology 1–13. Many papers have been appeared on the problem of existence of solutions of nonlinear random integral equations and the results are established by applying various fixed point techniques. These methods are broadly classified into three categories:. I admissibility theory, 2, 7, 24, 27, 41–47 , ii random contractor method, 17, 21, 35, 47–52 , iii measure of noncompactness method, 11, 53–61 All these methods are effectively used to study the existence of solutions for stochastic integral equations. In this paper we will study the existence of random solutions of nonlinear stochastic integral equations of mixed type. The results generalize the previous results of 2, 7, 24, 27, 41–46
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