Existence theorems of random solutions to stochastic functional integral equations

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

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On a class of stochastic functional integral equations

Colloquium Mathematicum ◽

10.4064/cm-35-1-141-146 ◽

1976 ◽

Vol 35 (1) ◽

pp. 141-146 ◽

Cited By ~ 8

Author(s):

A. N. V. Rao ◽

Chris P. Tsokos

Keyword(s):

Integral Equations ◽

Functional Integral ◽

Functional Integral Equations ◽

Stochastic Functional

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Nonlinear stochastic functional integral equations in the plane

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953395000335 ◽

1995 ◽

Vol 8 (4) ◽

pp. 371-379 ◽

Cited By ~ 2

Author(s):

Jan Turo

Keyword(s):

Global Existence ◽

Integral Equations ◽

Existence And Uniqueness ◽

Functional Integral ◽

Successive Approximations ◽

Uniqueness Theorems ◽

Existence And Uniqueness Theorems ◽

Global Existence And Uniqueness ◽

Functional Integral Equations ◽

Stochastic Functional

Local or global existence and uniqueness theorems for nonlinear stochastic functional integral equations are proved. The proofs are based on the successive approximations methods. The formulation includes retarded arguments and hereditary Volterra terms.

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Existence of Solutions of Infinite Systems of Nonlinear Functional Integral Equations of N-Variables in C(I × I ×⋯ × I,m(ϕ))

Asian-European Journal of Mathematics ◽

10.1142/s1793557121501473 ◽

2020 ◽

pp. 2150147

Author(s):

Hojjatollah Amiri Kayvanloo ◽

Reza Allahyari

Keyword(s):

Integral Equations ◽

Measure Of Noncompactness ◽

Existence Of Solutions ◽

Existence Theorems ◽

Functional Integral ◽

Hausdorff Measure Of Noncompactness ◽

Nonlinear Functional ◽

Infinite Systems ◽

Condensing Operators ◽

Functional Integral Equations

The aim of this paper is to investigate the solvability of infinite systems of nonlinear functional integral equations of [Formula: see text]-variables in [Formula: see text] by using the Hausdorff measure of noncompactness with the help of Meir–Keeler condensing operators. We also provide an illustrative example in support of our existence theorems.

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