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The purpose of the paper is to study the uniqueness problems of certain type of difference polynomial sharing a small function. We point out and rectify some gaps in the proof of the main results in [8]. In addition to this we obtain our main result as a corrected and generalized version of [8] in a more compact way which in turn improve a number of earlier results.

We investigate the uniqueness problem of entire functions that share two polynomials with their kth derivatives and obtain some results which improve and generalize the recent result due to Lü and Yi (2011). Also, we exhibit some examples to show that the conditions of our results are the best possible. [ABSTRACT FROM AUTHOR]

In this paper with the notion of weighted sharing of values we study the uniqueness of nonlinear differential polynomials of meromorphic functions sharing a nonzero polynomial and obtain two results which improves and generalizes the results due to L. Liu [Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 56 (2008), 3236-3245.] and P. Sahoo [Uniqueness and weighted value sharing of meromorphic functions, Applied. Math. E-Notes., 11 (2011), 23-32.].

The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation fn(z) + Pd(z, f) = p1(z)eα1(z) + p2(z)eα2(z), where Pd(z, f) is a difference-differential polynomial in f(z) of degree d 6 n-1 with small functions of f(z) as its coefficients, p1, p2 are nonzero rational functions and α1, α2 are nonconstant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation. [ABSTRACT FROM AUTHOR]

In connection to a conjecture of W. Lü, Q. Li and C.Yang (2014), we prove a result on small function sharing by a power of a meromorphic function with few poles with a derivative of the power. Our results improve a number of known results. [ABSTRACT FROM AUTHOR]

In this paper, we use the idea of normal family to investigate the problem of entire function that share entire function with its first derivative. [ABSTRACT FROM AUTHOR]

We establish some uniqueness results for meromorphic functions when two onlinear differential polynomials share a nonzero polynomial with certain degree and our results improve and generalize some recent results in Y.-H.Cao, X.-B. Zhang (2012). Also we exhibit two examples to show that the conditions used in the results are sharp. [ABSTRACT FROM AUTHOR]

In this paper, we use the idea of normal family to investigate the problem of meromorphic function having finitely many poles that share entire functions IM with its first derivative. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to study the possible uniqueness relation of entire functions when the difference polynomial generated by them sharing a non zero polynomial of certain degree. The result obtained in the paper will improve and generalize a number of recent results in a compact and convenient way. [ABSTRACT FROM AUTHOR]

In the paper, we use the idea of normal family to investigate the uniqueness problems of entire functions when certain types of differential-difference polynomials generated by them sharing a non-zero polynomial. Also we exhibit one example to show that the conditions of our results are the best possible. [ABSTRACT FROM AUTHOR]

With the idea of normal family we study the uniqueness of meromorphic functions f and g when fn(f(k))m -- p and gn(g(k))m -- p share two values, where p is any nonzero polynomial. The result of this paper significantly improves and generalizes the result due to A.Banerjee and S.Majumder (2018). [ABSTRACT FROM AUTHOR]

In this paper, we use the idea of normal family to investigate the situation when a power of a combination of transcendental meromorphic function with its shift shares small function with it's derivative and obtain three results which improve and generalize the recent result due to Lü and Yi [12]. Also we exhibit some examples to fortify the condition of our results. [ABSTRACT FROM AUTHOR]