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Appell, J., Guanda, N. and Väth, M. (2011) Function Spaces with the Matkowski Property and Degeneracy Phenomena for Composition Operators. Fixed Point Theory, 12, 265-284.

has been cited by the following article:

• TITLE: The Space of Bounded p(·)-Variation in the Sense Wiener-Korenblum with Variable Exponent

  AUTHORS: O. Mejía, N. Merentes, J. L. Sánchez, M. Valera-López

  KEYWORDS: Generalized Variation, p(·)-Variation in the Sense of Wiener-Korenblum, Exponent Variable, Composition Operator, Matkowski’s Condition

  JOURNAL NAME: Advances in Pure Mathematics, Vol.6 No.1, January 19, 2016

  ABSTRACT: In this paper we present the notion of the space of bounded p(·)-variation in the sense of Wiener-Korenblum with variable exponent. We prove some properties of this space and we show that the composition operator H, associated with , maps the into itself, if and only if h is locally Lipschitz. Also, we prove that if the composition operator generated by maps this space into itself and is uniformly bounded, then the regularization of h is affine in the second variable, i.e. satisfies the Matkowski’s weak condition.