Operational properties involving functions with generalized continuity

Authors

DOI:

https://doi.org/10.14393/BEJOM-v4-2023-69041

Keywords:

Generalized continuity, Continuator, Continuant

Abstract

In the work [11], Vieira introduced a new perspective about continuity of functions, which involves the idea of a suitable type of continuity of a function with respect to another function. The inspiration for this notion of generalized continuity arises naturally from the concept of generalized limit of a function with respect to another function, thus expanding the field of mathematical knowledge about continuity of functions. Initially presented by Vieira and Braz in [1], the concept of generalized limit is relevant, since a Riemann integral is a case of a generalized limit, as can be seen in [11]. This article proposes to further explore this notion of generalized continuity and its main focus is to investigate and present operational properties that arise when we deal with functions that exhibit this generalized continuity, operational properties such as composition, concatenation, among others. Through this study, it is hoped to shed light on the meaning and implications of these properties in this context of generalized continuity, allowing a broader understanding of this notion of continuity.

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Author Biographies

Matheus Silveira Campos, Universidade Estadual de Campinas

Has a degree in Mathematics (Bachelor’s degree) from the Institute of Exact and Natural Sciences of Pontal (ICENP) of the Federal University of Uberlândia (UFU) (2022). He is currently a master’s student at the Institute of Mathematics, Statistics and Scientific Computing (IMECC) of the State University of Campinas (Unicamp), being a CNPq fellow since 08/2022 and researching in the area of Analysis and Differential Geometry.

Marcelo Gonçalves Oliveira Vieira, Universidade Federal de Uberlândia

He holds a degree in Mathematics from the Federal University of Uberlândia - UFU (2003), a master’s degree in Mathematics from the State University of Campinas - UNICAMP (2005) and a PhD in Mathematics from the State University of Campinas - UNICAMP (2009). Since March 2009, he has been a professor at the Federal University of Uberlândia (UFU), being assigned since 2018 to the Institute of Exact and Natural Sciences of Pontal (ICENP). He currently holds the position of Associate Professor III and has experience in the areas of Topology and Stochastic Systems, with emphasis on the following topics: generalized continuity, monotonic homotopies and Young’s systems.

José Henrique Souza Braz, Prefeitura Municipal de Ituiutaba

Has a degree in Mathematics (licentiate) from the Integrated Sciences Faculty of Pontal (FACIP) of the Federal University of Uberlândia (UFU)(2015). Acted as a scholarship holder of the Tutorial Education Program (PET - MEC/SESu) from September 2011 to August 2015. Has a master’s degree from the Postgraduate Program in Mathematics (Master’s) of the Mathematics Faculty of the Federal University of Uberlândia. Currently is a Basic Education Teacher (6th to 9th grade) of the Municipal Prefecture of Ituiutaba - MG.

References

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VIEIRA, M. G. O. Topological aspects of continuity via generalized limit, Brazilian Electronic Journal of Mathematics, v.2, n.3, p. 70-107, 2021. Available in: https://doi.org/10.14393/BEJOM-v2-n3-2021-55291. Accessed on Oct 12, 2023.

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Published

2023-10-20

How to Cite

CAMPOS, M. S.; VIEIRA, M. G. O.; BRAZ, J. H. S. Operational properties involving functions with generalized continuity. BRAZILIAN ELECTRONIC JOURNAL OF MATHEMATICS, Uberlândia, v. 4, p. 1–20, 2023. DOI: 10.14393/BEJOM-v4-2023-69041. Disponível em: https://seer.ufu.br/index.php/BEJOM/article/view/69041. Acesso em: 26 nov. 2024.

Issue

Vol. 4 (2023): Brazilian Electronic Journal of Mathematics

Section

Articles - Pure Mathematics

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