The lack of memory property in the density form

The celebrated lack of memory property is a unique property of the exponential distribution in the continuous domain. It is expressed in terms of equality of residual survival function with the survival function of the original distribution. We propose to extend this lack of memory property in terms of probability density function and examine therefrom its characterization and stability properties. In this process the density version of the lack of memory property can be interlinked with reciprocal coordinate subtangent of the density curve and a few other derived measures.