# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Existence and global attractivity of solutions of a nonlinear functional integral equation. (English) Zbl 1191.45004

The authors prove a result on the existence and global attractivity of solutions of a nonlinear functional integral equation. They generalize and extend several results concerning attractivity of solutions of some functional integral equations obtained earlier.

Two examples illustrating the main result are also given.

##### MSC:
 45G10 Nonsingular nonlinear integral equations 45M10 Stability theory of integral equations
##### References:
 [1] Agarwal, R. P.; Benchohra, M.; Seba, D.: On the application of measure of noncompactness to the existence of solutions for fractional differential equations, Results math. 55, 221-230 (2009) · Zbl 1196.26009 · doi:10.1007/s00025-009-0434-5 [2] Agarwal, R. P.; O’regan, D.: Infinite interval problems for differential, difference and integral equations, (2001) [3] Balachandran, K.; Julie, D.: Asymptotic stability of solutions of nonlinear integral equations, Nonlinear funct. Anal. appl. 2, 313-322 (2008) · Zbl 1162.45006 [4] Banaś, J.; Cabrera, I. J.: On existence and asymptotic behaviour of solutions of a functional integral equation, Nonlinear anal. 66, 2246-2254 (2007) · Zbl 1128.45004 · doi:10.1016/j.na.2006.03.015 [5] Banaś, J.; Dhage, B. C.: Global asymptotic stability of solutions of a functional integral equation, Nonlinear anal. 69, 1945-1952 (2008) · Zbl 1154.45005 · doi:10.1016/j.na.2007.07.038 [6] Banaś, J.; Goebel, K.: Measures of noncompactness in Banach space, Lecture notes in pure and applied mathematics 60 (1980) · Zbl 0441.47056 [7] Banaś, J.; Rzepka, B.: An application of measures of noncompactness in the study of asymtotic stability, Appl. math. Lett. 16, 1-6 (2003) · Zbl 1015.47034 · doi:10.1016/S0893-9659(02)00136-2 [8] Banaś, J.; Sadarangani, K.: Solutions of some functional integral equations in Banach algebra, Math. comput. Modell. 38, 245-250 (2003) · Zbl 1053.45007 · doi:10.1016/S0895-7177(03)90084-7 [9] Burton, T. A.: Volterra integral and differential equations, (1983) [10] Burton, T. A.: A fixed point theorem of Krasnoselskii, Appl. math. Lett. 11, 85-88 (1998) · Zbl 1127.47318 · doi:10.1016/S0893-9659(97)00138-9 [11] Darwish, M. A.: On global attractivity of solutions of a functional integral equation, Electr. J. Qual. theory diff. Equat. 21, 1-10 (2007) · Zbl 1178.45005 · doi:emis:journals/EJQTDE/2007/200721.html [12] Darwish, M. A.: On solvability of some quadratic functional – integral equation in Banach algebra, Commun. appl. Anal. 11, 441-450 (2007) · Zbl 1137.45004 [13] Dhage, B. C.: A fixed point theorem in Banach algebras with applications to functional integral equations, Kyungpook math. J. 44, 145-155 (2004) [14] Dhage, B. C.; Lakshmikantham, V.: On global existence and attractivity results for nonlinear functional integral equations, Nonlinear anal. 72, 2219-2227 (2010) · Zbl 1197.45005 · doi:10.1016/j.na.2009.10.021 [15] Julie, D.; Balachandran, K.: Asymptotic behaviour of solutions to functional integral equation with deviating arguments, Electr. J. Differ. equat. 2008, 1-9 (2008) · Zbl 1165.45009 · doi:emis:journals/EJDE/Volumes/2008/77/abstr.html [16] 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 · doi:10.1016/j.jmaa.2005.08.010 [17] Krasnosel’skii, M. A.: Topological methods in the theory of nonlinear integral equations, (1964) · Zbl 0111.30303 [18] Liu, Z.; Kang, S. M.: Existence and asymptotic stability of solutions to a functional integral equation, Taiwanese J. Math. 11, 187-196 (2007) · Zbl 1145.45003 [19] Olszowy, L.: Solvability of some functional integral equation, Dynam. syst. Appl. 18, 667-676 (2009) · Zbl 1184.45003 [20] Smart, D. R.: Fixed point theorems, (1980)