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Article

Caballero, J. ; O'Regan, D. ; Sadarangani, K. B.
On monotonic solutions of some integral equations. (English). Archivum Mathematicum, vol. 41 (2005), issue 3, pp. 325-338
MSC: 45G10, 45M99, 47H09, 47H30, 47N20 | MR 2188387 | Zbl 1122.45008
Keywords:
measure of noncompactness; fixed point theorem; monotonic solutions
Summary:
The aim of this paper is to obtain monotonic solutions of an integral equation of Urysohn-Stieltjes type in $C[0,1]$. Existence will be established with the aid of the measure of noncompactness.
References:
[1] Argyros I. K.: On a class of quadratic integral equations with perturbations. Funct. Approx. Comment. Math. 20 (1992), 51–63. MR 1201716
[2] Banás J., Goebel K.: Measures of noncompactness in Banach Spaces. Marcel Dekker, New York and Basel 1980. MR 0591679 | Zbl 0441.47056
[3] Banás J., Olszowy L.: Measures of noncompactness related to monotonicity. Ann. Soc. Math. Pol., Commentat. Math. 41 (2001), 13–23. MR 1876707 | Zbl 0999.47041
[4] Banás J., Rodríguez J. R., Sadarangani K.: On a class of Urysohn-Stieltjes quadratic integral equations and their applications. J. Comput. Appl. Math. 113 (2000), 35–50. MR 1735811 | Zbl 0943.45002
[5] Busbridge I. W.: On the $H$-function of Chandrasekhar. Quart. J. Math. Oxford Ser. (2) 8 (1957), 133–140. MR 0100208
[6] Chandrasekhar S.: The transfer of radiation in stellar atmospheres. Bull. Amer. Math. Soc. 53 (1947), 641–711. MR 0022303
[7] Chandrasekhar S.: Radiative Transfer. Oxford Univ. Press London, 1950. MR 0042603 | Zbl 0037.43201
[8] Crum M.: On an integral equation of Chandrasekhar. Quart. J. Math. Oxford Ser. (2) 18 (1947), 244–252. MR 0023437 | Zbl 0029.26901
[9] Darbo G.: Punti uniti in transformazioni a condominio non compatto. Rend. Sem. Mat. Univ. Padova 24 (1955), 84–92. MR 0070164
[10] Dunford N., Schwartz J.: Linear Operators I. Int. Publ. Leyden, 1963.
[11] Kelly C.: Approximation of solutions of some quadratic integral equations in transport theory. J. Integral Equations 4 (1982), 221–237. MR 0661170
[12] Kuratowski K.: Sur les espaces completes. Fund. Math. 15 (1930), 301–309.
[13] Natanson I.: Theory of functions of a real variable. Ungar, New York, 1960.
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