Applied Mathematics, 2017, 8, 846-856 http://www.scirp.org/journal/am ISSN Online: 2152-7393 ISSN Print: 2152-7385 DOI: 10.4236/am.2017.86066 June 28, 2017 Solvability of Chandrasekhar’s Quadratic Integral Equations in Banach Algebra Hind H. G. Hashem 1 , Aml A. Alhejelan 2 1 Faculty of Science, Alexandria University, Alexandria, Egypt 2 Collage of Science, Qassim University, Buraidah, KSA Abstract In this paper, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contain various integral and functional equations that are considered in nonlinear analysis. Our con- siderations will be discussed in Banach algebra using a fixed point theorem instead of using the technique of measure of noncompactness. An important special case of that functional equation is Chandrasekhar’s integral equation which appears in radiative transfer, neutron transport and the kinetic theory of gases [1]. Keywords Nonlinear Operators, Banach Algebra, Chandrasekhar’s Integral Equations 1. Introduction Functional integral and differential equations of different types play an im- portant and a fascinating role in nonlinear analysis and finding various ap- plications in describing of several real world problems[2] [3] [4] [5] [6] [7] [8] [9]. Nonlinear functional integral equations have been discussed in the literature extensively, for a long time. See for example, Subramanyam and Sundersanam [10], Ntouyas and Tsamatos [11], Dhage and O’Regan [12] and the references therein. Dhage [12] and [13] initiated the study of nonlinear integral equations in a Banach algebra via fixed point techniques instead of using the technique of measure of noncompactness. Dhage [14] studied the existence of the nonlinear functional integral equation (in short FIE) How to cite this paper: Hashem, H.H.G. and Alhejelan, A.A. (2017) Solvability of Chandrasekhar’s Quadratic Integral Equa- tions in Banach Algebra. Applied Mathe- matics, 8, 846-856. https://doi.org/10.4236/am.2017.86066 Received: May 9, 2017 Accepted: June 25, 2017 Published: June 28, 2017 Copyright © 2017 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access