On $f$-strongly Cesàro and $f$-statistical derivable functions

In 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 Cesàro 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 Cesàro derivative is related to the strongly Cesàro derivative and to the $f$-statistical derivative. Under suitable conditions of the modulus $f$, several characterizations involving the previous concepts have been obtained.