Somewhat Mr-continuous and Somewhat Mr-open Functions

Abstract

The present article introduces and investigates new classes of functions, namely somewhat mr-continous and somewhat mr-open functions, by utilizing minimal regular open sets and minimal regular closed sets. The paper establishes the relationship between these new categories and other classes of functions, such as somewhat continuous, somewhat r-continuous and completely continuous functions, while also providing examples, counter examples, and various properties. The study of these classes of functions represents a significant contribution to the field of mathematics and provides new insights into the properties and behaviour of functions in various contexts.