## Abstract

This investigation is carried out by the inspiration of noteworthy results pertaining to approximate Lie \(\star \)-derivations connected with various additive, quadratic, cubic, quartic functional equations. For the first time, we study the stabilities of reciprocal Lie \(\star \)-derivations and reciprocal-quadratic Lie \(\star \)-derivations in the setting of normed \(\star \)-algebras through direct method. The stabilities associated with different upper bounds are also discussed. In addition, we present the relationship of reciprocal derivations dealt in this study with automorphism. The comparative study of stability results obtained in this investigation is also discussed at the end of this paper.

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## Funding

The first two authors are supported by the Research Council, Oman (Under Project Proposal ID: BFP/RGP/CBS/18/099). The third author is supported by the Science and Engineering Research Board, India, under MATRICS Scheme (F. No.: MTR/2020/000534).

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Kumar, B.V.S., Al-Shaqsi, K. & Dutta, H. Approximate reciprocal Lie \(\star \)-Derivations.
*Soft Comput* **25, **14969–14977 (2021). https://doi.org/10.1007/s00500-021-06395-9

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### Keywords

- Reciprocal functional equation
- Lie derivation
- Lie \(\star \)-derivation
- Generalized Ulam–Hyers stability