Singularity free analysis of a self-similar model of proton structure function at small $\mathit{\text{x}}$

In this paper we make re-analysis of a self-similarity based model of the proton structure function at small $\mathit{\text{x}}$ pursued in recent years. The additional assumption is that it should be singularity free in the entire kinematic range $0<\mathit{\text{x}}<1$. Our analysis indicates that the model is valid in a more restrictive range of $Q^2$. We also discuss the possibility of incorporation of Froissart saturation condition in the model.