Partial sharing of small functions with exact difference

Abstract

We have proven certain uniqueness results related owing to the partial sharing of small functions of $f$ with difference polynomials of the form $L(f)=b_k(z)f(z+kc)+\ldots +b_0(z)f(z)$, where $b_i$ are small functions of $f$. As a consequence of this, we have deduced the conditions under which, $f$ is identically equal to its exact difference operator $\Delta_c^k f$.

Keywords

• meromorphic functions, difference polynomials, partial sharing