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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.
In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. We give also some examples which show that the obtained results are applicable
We study nonlinear singular integral equation of Volterra type in Banach space of real functions defined and continuous on a bounded and closed interval. Using a suitable measure of noncompactness we prove the existence of monotonic solutions of the considered equation and its generalization. We illustrate our existence results by numerical examples.
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.
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.
In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of asymptotically stable solutions of some nonlinear functional integral equations in the space of continuous and bounded functions on R+ = [0,∞). We also give some examples satisfying the conditions our existence theorem.
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 : C → C has a fixed point. As its application, we give an existence result for the solution of an integral equation.
