Uniqueness Results Between the Derivatives of a Linear Shift and Meromorphic Functions

Authors: Jayashri Pattar

Country: India

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Abstract: The uniqueness of a meromorphic function f(z) and its shift f(z+c) under various value-sharing and growth conditions has been extensively studied. In particular, the uniqueness of their derivatives under IM and CM value-sharing conditions has received considerable attention. In this paper, we investigate the uniqueness of f^((l)) (z) and L^((k)) (f) when they share two distinct values CM. Where L(f)=∑_(j=1)^n▒〖a_j f(z+c_j)〗 be a linear shift function of f(z). Our results refine and extend existing uniqueness theorems. We also study the role of deficiency conditions in value sharing and their impact on uniqueness. Finally, we establish uniqueness results for f^((l)) (z) and L^((k)) (f) sharing one value CM under suitable deficiency conditions, and obtain the corresponding IM result under a stronger deficiency condition.

Keywords: meromorphic function, uniqueness, linear, value sharing, shift function.

Paper Id: 233229

Published On: 2026-10-03

Published In: Volume 14, Issue 5, September-October 2026

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