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.
"Maximal Classes for the Family of [λ,ρ]-Continuous Functions." Real Anal. Exchange 36 (2) 307 - 324, 2010/2011.