Uniqueness results for the difference operators using the conception of sharing value

In this article we considered a difference-differential polynomial of a transcendental entire function and established in the first two theorems criteria for infinitely many solutions for such type of equation. In the 3rd and 4th theorems we introduced $k$-th order differentiation of a polynomial of a transcendental entire function and its difference operator, and developed some uniqueness results in different aspects using the conception of sharing value. We elaborated our results with some remarks and analysed the results in different aspects and conditions. The results generalize and improve previous results of Zhang–Lin and Benerjee–Majumder. We introduced some notes to draw the gravity of improvement and generalisation of the previous results.