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

In this paper we make re-analysis of a self-similarity based model of the proton structure function at small \textit{x} pursued in recent years. The additional assumption is that it should be singularity free in the entire kinematic range $0<\textit{x}<1$. 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.