@article{Arenas Jaffeth2024, 
author = {Cure Arenas Jaffeth and Ferrer Sotelo Kandy and Ferrer Villar Osmin},
title = {Functions of bounded  (2,k)-variation in 2-normed spaces},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {24166-24183},
keywords = {2-product, 2-norm, 2-Hilbert, 2-Banach, (2, k)-variation},
url = {https://www.sciopen.com/article/10.3934/math.20241175},
doi = {10.3934/math.20241175},
abstract = {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, 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 are presented that enrich the results obtained in this work (4.1 and 4.2).}
}