On the Existence and Global Attractivity of Solutions of a Functional Integral Equation

Using the concept of measure of noncompactness, we present some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation. Our results improve and extend some previous known results and based on weaker conditions. Some examples which show that our results are applicable when the previous results are inapplicable are also included.

• Asadollah Aghajani
• Yaghoub Jalilian

• Functional integral equation
• fixed-point
• measure of noncompactness
• attractive solution
• asymptotic stability.

[1] J. Bana's, B.c. Dhage, Global asymptotic stability of solutions of
a functional integral equation, Nonlinear Analysis. 69(2008)1949-
1952.
[2] J. Bana's, B. Rzepka, An application of a measure of noncompactness
in the study of asymptotic stability, Applied Mathematic
Letters. 16(203)1-6.
[3] J. Bana's, K. Goebel, Measures of Noncompactness in Banach
Space, in: Lecture Notes in Pure and Applied Mathematics, vol.
60, Dekker, New York, 1980.
[4] J. Bana's, Measures of noncompactness in the space of continuous
tempered functions, Demonstratio Math. 14(1981)127133.
[5] H. Hochstadt, Integral Equations, John Willy and Sons 1973.
[6] Z. Liu, S.M. Kang, Existance and asymptotic stablity of solutions
to functional-integral equation, Taiwanese Journal of Mathematics.
11(2007)187-196.
[7] F.G. Tricomi, Integral Equations, University Press Cambridge
1957.