<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span style="font-size: 9pt; font-family: NimbusRomNo9L;">A symmetric bi-additive mapping&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">F</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">, on a prime ring&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">R&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">is called skew symmetric Jordan bi-derivation (</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">SSJBD</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">) if the following equality (associated with the automorphism of&nbsp;</span><span style="font-size: 9pt; font-family: rtxmi;">α&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">of&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">R</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">):</span></p><p><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">F</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">(</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">x</span><span style="font-size: 6pt; font-family: NimbusRomNo9L; vertical-align: 4pt;">2</span><span style="font-size: 9pt; font-family: rtxmi;">,&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">z</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">)&nbsp;</span><span style="font-size: 9pt; font-family: rtxr;">=&nbsp;</span><span style="font-size: 9pt; font-family: rtxmi;">α</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">(</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">x</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">)</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">F</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">(</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">x</span><span style="font-size: 9pt; font-family: rtxmi;">,&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">z</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">)&nbsp;</span><span style="font-size: 9pt; font-family: rtxr;">+&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">F</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">(</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">x</span><span style="font-size: 9pt; font-family: rtxmi;">,&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">z</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">)</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">x<br></span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">is satisfied. The paper aims to investigate the properties of&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L; font-style: italic;">SSJBD&nbsp;</span><span style="font-size: 9pt; font-family: NimbusRomNo9L;">constructed by a generalization of symmetric Jordan bi-</span></p><p><span style="font-size: 9pt; font-family: NimbusRomNo9L;">derivations on prime rings.<br></span></p></div></div></div>