Abstract
Our paper focuses on exploring transcendental entire solutions of various types of \(q\)-shift binomial and trinomial Fermat-type equations. Additionally, we extend the investigation to simultaneous equations involving \(q\)-shift, taking into account the complexity and feasibility of analyzing these equations. We have identified and highlighted important observations that differentiate these \(q\)-shift equations from their analogous shift equations. In addition to transcendental entire solutions, we have also ventured into finding meromorphic solution for certain types of \(q\)-shift equations. To support our results and conclusions, we provide a series of examples to demonstrate the validity of our findings in terms of the transcendental entire and meromorphic solutions we have discovered.
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The second author is thankful to Council of Scientific and Industrial Research (India, for financial help under File no. 09/0106(13572)/2022-EMR-I).
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Banerjee, A., Sarkar, J. On Transcendental Entire Solution of Ordinary and Systems of Different Genre of Fermat-type \(\boldsymbol{q}\)-Shift Equations. Lobachevskii J Math 44, 5179–5192 (2023). https://doi.org/10.1134/S1995080223120089
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DOI: https://doi.org/10.1134/S1995080223120089