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In this paper, the real dynamics of one parameter family of functions h λ (x)=λxe x (ex-1), λ&gt;0 is investigated. It is shown that the real fixed point of h λ (x) exists only for 0 1 It is found that the whole real line converges to real attracting fixed point of h λ (x) for 0&lt;λ&lt;1.

Real Dynamics of Family of Functions λxex/(ex-1) for Positive λ

Real Dynamics of Family of Functions λxe^x/(e^x-1) for Positive λ