In this paper, we prove that if a globally Lipschitz non-autonomous superposition operator maps the space of functions of bounded second $ \kappa $-variation into itself then its generator function satisfies a Matkowski condition. We also provide conditions for the existence and uniqueness of solutions of the Hammerstein and Volterra equations in this space.
Citation: Jurancy Ereú, Luz E. Marchan, Liliana Pérez, Henry Rojas. Some results on the space of bounded second κ-variation functions[J]. AIMS Mathematics, 2023, 8(9): 21872-21892. doi: 10.3934/math.20231115
In this paper, we prove that if a globally Lipschitz non-autonomous superposition operator maps the space of functions of bounded second $ \kappa $-variation into itself then its generator function satisfies a Matkowski condition. We also provide conditions for the existence and uniqueness of solutions of the Hammerstein and Volterra equations in this space.
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Jurancy Ereú, Luz E. Marchan, Liliana Pérez, Henry Rojas. Some results on the space of bounded second κ-variation functions[J]. AIMS Mathematics, 2023, 8(9): 21872-21892. doi: 10.3934/math.20231115
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