Weighted EP elements with respect to a pair of elements in a ring

We introduce the novel concept of weighted EP-elements with respect to two elements in a ring to establish a unified framework that naturally generalizes classical EP elements. We then characterize the fundamental properties of weighted EP elements, demonstrating that many classical properties extend to this general setting with two weights. The relations among the weighted EP-element, the weighted group inverse, the weighted core inverse, and the weighted Moore-Penrose inverse are thereby established.