In this paper, we provide in a general Hilbert space new characterizations of uniform prox-regularity involving outside but sufficiently close points considered sets. We show that the complement prox-regular set is nothing union closed balls with common radius. derive from given equivalent to semiconvexity property its distance function. Various estimates metric projection mapping are also esta...

‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...