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In this paper, we introduce the concepts of super-stability, stability, δ -Ger-stability of the exponential equation of an operator from a normed space into a normed algebra. By using some results due to J. Baker and R. Ger, we obtain some new conclusions about these stabilities. Mathematics subject classification (2010): Primary 39B52, secondary 39B82, 46B99, 17A40.

Super-stability and stability of the exponential equations