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Global attractivity results for nonlinear functional integral equations via a Krasnoselskii type fixed point theorem. (English) Zbl 1163.45005
The author derives sufficient conditions for the global attractivity and the global asymptotic attractivity of the solutions of a nonlinear functional integral equation of Volterra type on the half-line.

45G10Nonsingular nonlinear integral equations
45M05Asymptotic theory of integral equations
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] Banas, J.; Dhage, B. C.: Global asymptotic stability of solutions of a functional integral equations. Nonlinear anal. (2007)
[2] Banas, J.; Rzepka, B.: An application of measures of noncompactness in the study of asymptotic stability. Appl. math. Lett. 16, 1-6 (2003)
[3] Burton, T. A.: Volterra integral and differential equations. (1983) · Zbl 0515.45001
[4] Burton, T. A.: A fixed point theorem of Krasnoselskii. Appl. math. Lett. 11, 85-88 (1998) · Zbl 1127.47318
[5] Dhage, B. C.: A fixed point theorem in Banach algebras with applications to functional integral equations. Kyungpook math. J. 44, 145-155 (2004) · Zbl 1057.47062
[6] Dhage, B. C.: Local asymptotic attractivity for nonlinear quadratic functional integral equations. Nonlinear anal. (2008) · Zbl 1182.47058
[7] B.C. Dhage, Asymptotic stability of nonlinear functional integral equations via measures of noncompactness, preprint · Zbl 1160.47041
[8] Hu, X.; Yan, J.: The global attractivity and asymptotic stability of solution of a nonlinear integral equation. J. math. Anal. appl. 321, 147-156 (2006) · Zbl 1108.45006
[9] Kuczma, M.: Functional equations in single variable. Monografie math. 46 (1968) · Zbl 0196.16403
[10] Krasnoselskii, M. A.: Topological methods in the theory of nonlinear integral equations. (1964)
[11] O’regan, D.; Meehan, M.: Existence theory for nonlinear integral and integro-differential equations. (1998)
[12] Smart, D. R.: Fixed point theorems. (1980) · Zbl 0427.47036
[13] Väth, M.: Volterra and integral equations of vector functions. (2000) · Zbl 0940.45002
[14] Zeidler, E.: Nonlinear functional analysis and its applications: part I. (1985) · Zbl 0583.47051