Maximal Classes for the Family of [λ,ρ]-Continuous Functions

Abstract

In this paper we give the definition of \([\lambda,\varrho]\)-continuity of real-valued functions defined on an open interval, which is an example of path continuity. We give some properties of \([\lambda,\varrho]\)-continuous functions. The aim of the paper is to find the maximal additive class and the maximal multiplicative class for the family of \([\lambda,\varrho]\)-continuous functions.