Functions of bounded (2,k)-variation in 2-normed spaces

Functions of bounded (2,k)-variation in 2-normed spaces

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In this work, the notion of function of bounded variation in 2-normed spaces was established (Definition 4.2), the set of functions of bounded $ (2, k) $-variation was endowed with a norm (Theorem 4.5), and it was proved that such a set is a Banach space (Theorem 4.

6).In addition, Skincare the fundamental properties of the functions of bounded $ (2, k) $-variation in the formalism of 2-Hilbert and 2-normed spaces were studied (see Theorems 4.1, 4.

3, 4.4).Also, it was shown how to endow a 2-normed space with a function of bounded $ (2, k) $-variation from a classical Hilbert space (Proposition 4.

1).A series of examples and counterexamples Pull Along Toy are presented that enrich the results obtained in this work (4.1 and 4.

2).