@ARTICLE{10.21494/ISTE.OP.2023.1049, 

TITLE={On the solutions of Fermat type quadratic trinomial equations in ℂ<sup>2</sup> generated by first order linear C-SHIFT and partial differential operators}, 
  
AUTHOR={Abhijit Banerjee
, Jhuma Sarkar, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={15}, 

NUMBER={Issue 1 (January 2024)}, 
	
YEAR={2024}, 

URL={http://openscience.fr/On-the-solutions-of-Fermat-type-quadratic-trinomial-equations-in-%E2%84%822-generated}, 
	
DOI={10.21494/ISTE.OP.2023.1049}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={This article is devoted to explore various forms of transcendental entire solution of different quadratic trinomials generated by first order linear c-shift operator. We also investigate the forms of solutions of certain quadratic trinomials under linear and mixed partial differential operators. Our paper improves the results of Li-Xu [Axioms, 126(10)(2021), 1-19] in two directions. In addition, in a corollary, deducted from one of our main result, we extend a result of Zhang et al. [ Aims Math., 7(2022), 11597-11613]. A series of examples have been exhibited to justify the existence and forms of transcendental entire solution of such equations. In the last section of the paper we have put a relevant question for future research.}}