<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to be less than one. As the hyper-order is a crucial parameter that characterizes the growth of entire functions, it will be interesting to investigate this unexplored domain, as far as practible, with certain restriction on hyper order. Our results are the improvements of previous results reported in recent papers [<xref ref-type="bibr" rid="j_amsil-2023-0018_ref_012">12</xref>], [<xref ref-type="bibr" rid="j_amsil-2023-0018_ref_013">13</xref>]. We have provided a series of examples to demonstrate and validate the effectiveness of our proposed solutions.</p>
</abstract>

In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to be less than one. As the hyper-order is a crucial parameter that characterizes the growth of entire functions, it will be interesting to investigate this unexplored domain, as far as practible, with certain restriction on hyper order. Our results are the improvements of previous results reported in recent papers [12], [13]. We have provided a series of examples to demonstrate and validate the effectiveness of our proposed solutions.

On Transcendental Entire Solution of Fermat-Type Trinomial and Binomial Equations Under Restricted Hyper-Order

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to...

On Transcendental Entire Solution of Fermat-Type Trinomial and Binomial Equations Under Restricted Hyper-Order

Published Online: Nov 22, 2023

Page range: -

Received: Aug 22, 2023

Accepted: Oct 18, 2023

DOI: https://doi.org/10.2478/amsil-2023-0018

Keywords
Nevanlinna theory, entire solution, hyper-order, quadratic trinomial equation, transcendental solution

© 2023 Abhijit Banerjee et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On Transcendental Entire Solution of Fermat-Type Trinomial and Binomial Equations Under Restricted Hyper-Order

Published Online: Nov 22, 2023

Page range: -

Received: Aug 22, 2023

Accepted: Oct 18, 2023

DOI: https://doi.org/10.2478/amsil-2023-0018

KeywordsNevanlinna theory, entire solution, hyper-order, quadratic trinomial equation, transcendental solution

© 2023 Abhijit Banerjee et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Nevanlinna theory, entire solution, hyper-order, quadratic trinomial equation, transcendental solution