Altay, BilalGarcia-Pacheco, Francisco JavierKama, Ramazan2024-08-042024-08-0420222473-6988https://doi.org/10.3934/math.2022629https://hdl.handle.net/11616/100601In this manuscript, we introduce the following novel concepts for real functions related to f-convergence and f-statistical convergence: f-statistical continuity, f-statistical derivative, and f-strongly Cesaro derivative. In the first subsection of original results, the f-statistical continuity is related to continuity. In the second subsection, the f-statistical derivative is related to the derivative. In the third and final subsection of results, the f-strongly Cesaro derivative is related to the strongly Cesaro derivative and to the f-statistical derivative. Under suitable conditions of the modulus f, several characterizations involving the previous concepts have been obtained.eninfo:eu-repo/semantics/openAccessstatistical convergencef-statistical convergenceCesaro convergencestrongly Cesaro convergencediscrete derivativeArticle76112761129110.3934/math.20226292-s2.0-85128130220Q2WOS:000788060600006Q1