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Chandrasekhar’s and related equations , Bull. Austral. Math. Soc. , 32 ( 1985 ), 275 – 292 . [3] B urton , T. A. , Integral equations, implicit functions and fixed

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Agarwal, R. P., O’Regan, D. and Wong, P. J. Y. , Positive solutions of differential, difference and integral equations , Kluwer Academic Publishers, Dordrecht, (1999). MR 2000a :34046

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References 1 H u , S. , K havanin , M. and Z huang , W. , Integral equations arising in the kinetic theory of gases , Appl. Anal. , 34 ( 1989 ), 261 – 266

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The existence and uniqueness of solutions of more general Volterra-Fredholm integral equations are investigated. The successive approximations method based on the general idea of T. Wazewski is the main tool.

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Summary We discuss the existence or the existence and uniqueness of global and local Λ-bounded variation (ΛBV) solutions as well as continuous ΛBV-solutions of nonlinear Hammerstein and Volterra-Hammerstein integral equations formulated in terms of the Lebesgue integral. Since the space of functions of bounded variation in the sense of Jordan is a proper subspace of functions of Λ-bounded variation and for some class of functions φ, the space of functions of bounded φ-variation in the sense of Young is also a proper subspace of the space under consideration, our results extend known results in the literature.

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In this paper, we are going to obtain the spectral relations for the Fredholm integral equation of the first kind with certain singular kernel, by using Krein's method.

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Abstract  

We define an alternate convexically nonexpansive map T on a bounded, closed, convex subset C of a Banach space X and prove that if X is a strictly convex Banach space and C is a nonempty weakly compact convex subset of X, then every alternate convexically nonexpansive map T : CC has a fixed point. As its application, we give an existence result for the solution of an integral equation.

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