MATHEMATICA BOHEMICA, Vol. 133, No. 4, pp. 407-420 (2008)

On monotonic solutions of an integral equation
of Abel type

Mohamed Abdalla Darwish

Mohamed Abdalla Darwish, Department of Mathematics, Faculty of Science, Alexandria University at Damanhour, 22511 Damanhour, Egypt, e-mail: darwishma@yahoo.com

Abstract: We present an existence theorem for monotonic solutions of a quadratic integral equation of Abel type in $C[0,1]$. The famous Chandrasekhar's integral equation is considered as a special case. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.

Keywords: quadratic integral equation, monotonic solutions, Abel, measure of noncompactness, Darbo's fixed point theorem

Classification (MSC2000): 45G10, 45M99, 47H09

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