Inspired by a problem found in a textbook of Faddeev and Sominsky we propose a new form of roots of an arbitrary complex number. Our idea uses the zeros of some polynomials connected with the modified Chebyshev polynomials.
Abstract. We consider the Nemytskij operator, i.e., the operator of substitution, defined by (Νφ)(χ) := G (χ, φ(χ)), where G is a given multifunction. It is shown that Ν maps C 1 (7, C), the space of all continuously differentiable functions on the interval I with values in a cone C in a Banach space, into C 1 (I, cc(Z)), the space of all continuously differentiable set-functions on I with compact and convex values in a Banach space Ζ and Ν fulfils the Lipschitz condition if and only if the generator G is of the form
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