Operational properties involving functions with generalized continuity

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.