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Point fixe d'une application non contractante.

Pierre Gilles Lemarié-Rieusset (2006)

Revista Matemática Iberoamericana

We study a multilinear fixed-point equation in a closed ball of a Banach space where the application is 1-Lipschitzian: existence, uniqueness, approximations, regularity.

Practical Ulam-Hyers-Rassias stability for nonlinear equations

Jin Rong Wang, Michal Fečkan (2017)

Mathematica Bohemica

In this paper, we offer a new stability concept, practical Ulam-Hyers-Rassias stability, for nonlinear equations in Banach spaces, which consists in a restriction of Ulam-Hyers-Rassias stability to bounded subsets. We derive some interesting sufficient conditions on practical Ulam-Hyers-Rassias stability from a nonlinear functional analysis point of view. Our method is based on solving nonlinear equations via homotopy method together with Bihari inequality result. Then we consider nonlinear equations...

Properties of the Sobolev space H k s , s '

Henryk Kołakowski (1999)

Annales Polonici Mathematici

Let n ≥ 2 and H k s , s ' = u ∈ S ' ( ℝ n ) : ∥ u ∥ s , s ' < ∞ , where ∥ u ∥ ² s , s ' = ( 2 π ) - n ∫ ( 1 + | ξ | ² ) s ( 1 + | ξ ' | ² ) s ' | F u ( ξ ) | ² d ξ , F u ( ξ ) = ∫ e - i x ξ u ( x ) d x , ξ ' ∈ ℝ k , k < n. We prove that for some s,s’ the space H k s , s ' is a multiplicative algebra.

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