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

Abstract

<abstract><p>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.</p></abstract>