University of Guilan Journal of Algebra and Related Topics 2345-3931 9 2 2021 12 01 On some additive mappings on division rings 101 110 5303 10.22124/jart.2021.19142.1263 EN S. Ali Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India A. Abdelwanis Department of Mathematics Faculty of Science Cairo University Giza 12613, Egypt Journal Article 2021 03 11  Let $D$ be a division ring such that char$(D) \neq 2$  and $\alpha,\beta:D\rightarrow D$ be automorphisms of $D$. The main purpose of this paper is to characterizes additive maps                              <br />$f$ and $g$ satisfying the identity $f(x)\alpha(x^{-1}) + \beta(x)g(x^{-1}) = 0$ for all $0 \neq x\in D.$ As an application, we describe the structure of an additive map $f$ satisfying the identity                            <br />$f(x)\alpha(y)+\beta(x)f(y) =l$ for all $x,y\in D$ such that $xy=a,$ where $l,a\in D$ and $a$ is nonzero. With this, many known results can be either generalized or deduced. In particular, we generalized the results proved in<br />\cite{C1} and \cite{C2}, respectively.                                                                                                                                                                                            https://jart.guilan.ac.ir/article_5303_664350d6c417e151b54114b0e421bdfc.pdf