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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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] M aleknejad , K. , N ouri , K. and M ollapourasl , R. , Existence of solutions for some nonlinear integral equations , Commun. Nonlinear Sci. Numer. Simul. , 14 ( 2009 ), 2559 – 2564 . [9

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B anaś , J. and O lszowy , L. , On a class of measures of noncompactness in Banach algebras and their application to nonlinear integral equations , J. Appl. Anal. , 28 ( 2009 ), 1 – 24 . 21

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The peridynamic material model (PMM) is a new way to describe the material failures with discontinuities. Earlier works, presented by S. Silling, F. Bubaru and etc. introduced the Linear Elastic Fracture Mechanics of peridynamic material. In the recent work, the isotropic hardening plastic extension of PMM is presented. To solve the nonlinear integral equations of the problem the modified Newton method is used with mesh-less spatial discretization. At last some example shows the similarities and different between the results of classical and peridynamic plasticity.

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