On a class of iterative procedures for solving nonlinear equations in Banach spaces

Florian-Alexandru Potra

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Displaying similar documents to “On a class of iterative procedures for solving nonlinear equations in Banach spaces”

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We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the few available inertial-type methods for zeros of the sum of accretive operators in Banach spaces. ...

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How far is C(ω) from the other C(K) spaces?

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Let us denote by C(α) the classical Banach space C(K) when K is the interval of ordinals [1,α] endowed with the order topology. In the present paper, we give an answer to a 1960 Bessaga and Pełczyński question by providing tight bounds for the Banach-Mazur distance between C(ω) and any other C(K) space which is isomorphic to it. More precisely, we obtain lower bounds L(n,k) and upper bounds U(n,k) on d(C(ω),C(ωⁿk)) such that U(n,k) - L(n,k) < 2 for all 1 ≤ n, k < ω.