  In this paper, we study a natural modification of Sz\'{a}sz - Mirakjan
operators. It is shown by discussing many important established results for
Sz\'{a}sz - Mirakjan operators. The results do hold for this modification as
well, be they local in nature or global, be they qualitative or quantitative.
It is also shown that this generalization is meaningful by means of examples
and graphical representations.
