(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Using the concept of supra ε-open sets, this manuscript discusses and investigates new forms of supra continuity. More specifically, we introduce the concept of supra ε-continuous functions, which built upon the previous types of weaker forms of such notions. The relationships between our new class and existing previous supra continuity notions were examined using the diagram in Figure 1. Furthermore, the essential features of this concept are analyzed, as well as its analogous circumstances. Additionally, the notions of supra ε-irresolute functions and supra ε^*-cts functions were introduced. Moreover, we prove that the composition of supra ε-irresolute function and supra ε-cts function (respectively, supra ε-cts function and cts function is supra ε-cts, two supra ε-irresolute functions) is supra ε-cts (respectively, supra ε-cts, supra ε-irresolute). Also, we provide three new approaches for supra functions named supra ε-open functions, supra ε-closed functions, and supra ε-homeomorphism functions. We conclude with a detailed discussion of their key characteristics and provide several essential examples.