en عمومى General پژوهشي Research paper &lrm;&nbsp;<span style="color: #000000">Let </span><span style="color: #008000">$(X,d)$</span><span style="color: #000000"> be a metric space and </span><span style="color: #008000">$Jsubseteq (0,infty)$</span><span style="color: #000000"> be</span> <pre style="text-indent: 0px; margin: 0px; -qt-block-indent: 0"> <span style="color: #000000">a nonempty set. We study the structure of the arbitrary intersection of</span></pre> <pre style="text-indent: 0px; margin: 0px; -qt-block-indent: 0"> <span style="color: #000000">vector-valued </span><span style="color: #000000; text-decoration: underline">Lipschitz</span><span style="color: #000000"> algebras, and define a special Banach </span><span style="color: #000000; text-decoration: underline">subalgebra</span><span style="color: #000000"> of</span></pre> <pre style="text-indent: 0px; margin: 0px; -qt-block-indent: 0"> <span style="color: #008000">$cap{Lip_gamma (X,E):gammain J}$</span><span style="color: #000000">, where </span><span style="color: #008000">$E$</span><span style="color: #000000"> is a Banach algebra, denoted by </span><span style="color: #008000">$ILip_J (X,E)$</span><span style="color: #000000">. Mainly,</span></pre> <pre style="text-indent: 0px; margin: 0px; -qt-block-indent: 0"> <span style="color: #000000">we investigate </span><span style="color: #008000">$C-$</span><span style="color: #000000">character amenability of </span><span style="color: #008000">$ILip_J (X,E)$</span><span style="color: #000000">.</span></pre> <pre style="text-indent: 0px; margin: 0px; -qt-block-indent: 0; -qt-paragraph-type: empty"> </pre> Character amenability‎, ‎Lipschitz algebra‎, ‎Metric space‎, ‎Vector-valued functions. 191 205 http://ijmsi.ir/browse.php?a_code=A-10-3010-1&slc_lang=en&sid=1 M. Azizi m.azizi@sci.ui.ac.ir, mohsenazizi1366@chmail.ir 10031947532846007462 10031947532846007462 No Department of Mathematics, University of Isfahan, Isfahan, Iran. E. Biyabani rejali@gmail.com, rejali@sci.ui.ac.ir 10031947532846007463 10031947532846007463 Yes Department of Mathematics, University of Isfahan, Isfahan, Iran. A. Rejali A.Biyabani@iaumajlesi.ac.ir, biyabani91@yahoo.com 10031947532846007464 10031947532846007464 No Department of Mathematics, Islamic Azad University, majlesi Branch, Isfahan, Iran