Monotonicity theorems for some local systems (Q1322618)

The author considers local systems as described by \textit{B. Thomson} in ``Real functions'' (1985; Zbl 0581.26001). For such systems he introduces a condition (SD) motivated by a result of \textit{D. N. Sarkhel} and \textit{A. K. De} [J. Aust. Math. Soc., Ser. A 31, 26-45 (1981; Zbl 0477.26002)]. The paper includes several monotonicity theorems for functions with derivatives (defined with respect to the local system) fulfilling some natural conditions under the assumption that the system fulfills (SD). Also the relationship between the intersection condition and the condition (SD) is studied.