On Fuzzy Volterra Integral Equations with Deviating Arguments
نویسنده
چکیده
In 1982, Dubois and Prade [4, 5] first introduced the concept of integration of fuzzy functions. Kaleva [7] studied the measurability and integrability for the fuzzy set-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported by fuzzy sets in Rn. Existence of solutions of fuzzy integral equations has been studied by several authors [1, 2, 7, 8]. Subrahmanyam and Sudarsanam [13] proved existence theorems for fuzzy functional equations. They have used the embedding theorem of Kaleva [8], which is a generalization of the classical Rådström embedding theorem [11], and the Darbo fixed point theorem in the convex cone. Recently, Balachandran and Prakash [2, 3] studied the existence of solutions of nonlinear fuzzy Volterra-Fredholm integral equations. In this paper, we prove the existence of solutions of fuzzy Volterra integral equations with deviating arguments. The results, which generalize the results of [1, 2], are established with the help of the Darbo fixed point theorem. Further, we study the maximal solution of the fuzzy delay Volterra integral equation.
منابع مشابه
Spectral Scheme for Solving Fuzzy Volterra Integral Equations of First Kind
This paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classifications are considered based on the interval sign of the kernel. The Gauss-Legendre points and Legendre weights for arithmetics ...
متن کاملAPPLICATION OF FUZZY EXPANSION METHODS FOR SOLVING FUZZY FREDHOLM- VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND
In this paper we intend to offer new numerical methods to solvethe fuzzy Fredholm- Volterra integral equations of the firstkind $(FVFIE-1)$. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods.
متن کاملExistence and uniqueness of the solution of nonlinear fuzzy Volterra integral equations
In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.
متن کامل