en عمومى General پژوهشي Research paper In the&nbsp; $RC^*$-algebras and Lie $RC^*$-algebras, we approximate the homomorphisms and derivations<br> &nbsp; for&nbsp;the 3-variable Cauchy functional equation, by the fixed point method. Approximation, Functional equations, $RC^*$-algebras, Random space 163 177 http://ijmsi.ir/browse.php?a_code=A-10-568-2&slc_lang=en&sid=1 Y. Je Cho yjcho@gnu.ac.kr 10031947532846008799 10031947532846008799 No Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea Sh.-m. Shin-min smkang@gnu.ac.kr 10031947532846008800 10031947532846008800 No Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea T. M. Rassias trassias@math.ntua.gr 10031947532846008801 10031947532846008801 No Department of Mathematics National Technical University of Athens Zografou Campus, 157 80, Athens GREECE R. Saadati rsaadati@eml.cc 10031947532846008802 10031947532846008802 Yes Department of Mathematics, Iran University of Science and Technology, Tehran, Iran