An application of a diffeomorphism theorem to Volterra integral operator

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Using global diffeomorphism theorem based on duality mapping and mountain geometry, we investigate the properties of the Volterra operator given pointwise for t is an element of [0,1] by

V(x) (t) = x(t) + integral(t)(0) v(t, tau, x(tau))d tau, x(0) = 0.

Klíčová slova
diffeomorphism, Volterra integral operator, duality mapping