On the family of $[\lambda,\varrho]$-continuous functions

Abstract

In this paper, we introduce the class of 

$[\lambda, \varrho]$-continuous functions.
First, we investigate some relations beetwen the classes of $[\lambda_1, \varrho_1]$ and $[\lambda_2, \varrho_2]$-continuous functions
for different pairs $[\lambda_1, \varrho_1]$, $[\lambda_2, \varrho_2]$.
Next, we give an equivalent condition for a function in order that it will  belong to the disscused class.