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

Abhijit Banerjee; Jhuma Sarkar

doi:10.2478/amsil-2023-0018

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

Annales Mathematicae Silesianae

Volume 38 (2024): Issue 2 (September 2024)

By: Abhijit Banerjee and Jhuma Sarkar

Open Access

|Nov 2023

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.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2023-0018 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 177 - 194

Submitted on: Aug 22, 2023

Accepted on: Oct 18, 2023

Published on: Nov 22, 2023

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Nevanlinna theory,

entire solution,

hyper-order,

quadratic trinomial equation,

transcendental solution

Related subjects:

Mathematics,

General mathematics

© 2023 Abhijit Banerjee, Jhuma Sarkar, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 38 (2024): Issue 2 (September 2024)