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In this paper we establish the notion of the space of bounded  (p(⋅), 2)variation in De la Vallee Poussin-Wiener’s sense with variable exponent. We show some properties of this space and we show that any uniformly bounded composition operator that maps this space into itself necessarily satisfies the so-called Matkowski’s conditions.

advances in pure mathematics

Functions of Bounded (&amp;lt;i&amp;gt;p&amp;lt;/i&amp;gt;(&amp;amp;sdot;), 2)-Variation in De la Vall&amp;#233;e Poussin-Wiener’s Sense with Variable Exponent