Generalized Bihari Type Integral Inequalities and the Corresponding Integral Equations

László Horváth Department of Mathematics, University of Pannonia, Egyetem u. 10, 8200 Veszprém, Hungary Correspondence should be addressed to László Horváth, [email protected] Received 2 February 2009; Accepted 23 June 2009 Recommended by Alberto Cabada We study some special nonlinear integral inequalities and the corresponding integral equations in measure spaces. They are significant generalizations of Bihari type integral inequalities and Volterra and Fredholm type integral equations. The kernels of the integral operators are determined by concave functions. Explicit upper bounds are given for the solutions of the integral inequalities. The integral equations are investigated with regard to the existence of a minimal and a maximal solution, extension of the solutions, and the generation of the solutions by successive approximations. Copyright q 2009 László Horváth. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.