On the Additive Operators of type s and type a

Abstract:

      In theis paper, we introduce the concepts mentioned in the title. We have De Moivre's formula corresponding to the additive operator of type s. Boundedness, continuity and Frechet differentiability have been discussed. The necessary and sufficient conditions for the periodicity of the operators introduced are given. Two orthonormal (in the extended sense) systems of operators are obtained. The relation between the two types of operators is investigated and then Euler's formula and other new related formula are obtained.