MEAN VALUE THEOREMS FOR HOLOMORPHIC FUNCTIONS OF A GENERALIZED COMPLEX VARIABLE.

Generalized complex number systems generalize all unital real algebras of dimension two, including complex numbers, dual numbers, and double numbers. In this article, we have shown that the real part and the imaginary part of a holomorphic function of a generalized complex variable satisfy several forms of mean value theorem individually. In particular, as a corollary, these results hold true for complex holomorphic functions. [ABSTRACT FROM AUTHOR]