The authors study the existence and global attractivity of the solutions for the following nonlinear functional integral equation (FIE)
for all , where , , and .
They give two existence and global attractivity results for the solution of the FIE via a measure theoretic fixed point theorem of B. Dhage [Commun. Appl. Nonlinear Anal. 15, No. 2, 89–101 (2008; Zbl 1160.47041)]. These results improve and generalize the attractivity results of J. Banas and B. Rzepka [Appl. Math. Lett. 16, No. 1, 1–6 (2003; Zbl 1015.47034)], J. Banas and B. Dhage [Nonlinear Anal., Theory Methods Appl. 69, No. 7 (A), 1945–1952 (2008; Zbl 1154.45005)], B. Dhage [Nonlinear Anal., Theory Methods Appl. 70, No. 7 (A), 2485–2493 (2009; Zbl 1163.45005)] and X. Hu and J. Yan [J. Math. Anal. Appl. 321, No. 1, 147–156 (2006; Zbl 1108.45006)] under some weaker Lipschitz conditions.