| Summary: | 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.
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