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<p>In this paper, we have investigated the forms of solutions for Fermat-type quadratic trinomial equations governed by linear combinations of the function itself, its derivatives, and shifts. Our results rectify errors in a recent paper (Wang et al. in Bull Malays Math Sci Soc 43(4):2951–2965, 2020) by identifying several gaps within its analysis. Additionally, we consider <i>q</i>-shifts in similar quadratic trinomial equations, offering corrections to a related result from the same paper. Numerous examples are provided to illustrate the necessity and applicability of our findings.</p>

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On solutions of generalized quadratic differential difference equations

  • 期刊论文

  • 发表日期：

    2025年3月20日

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  • Abhijit Banerjee,
  • Jhuma Sarkar,
  • Goutam Haldar

摘要

In this paper, we have investigated the forms of solutions for Fermat-type quadratic trinomial equations governed by linear combinations of the function itself, its derivatives, and shifts. Our results rectify errors in a recent paper (Wang et al. in Bull Malays Math Sci Soc 43(4):2951–2965, 2020) by identifying several gaps within its analysis. Additionally, we consider q-shifts in similar quadratic trinomial equations, offering corrections to a related result from the same paper. Numerous examples are provided to illustrate the necessity and applicability of our findings.