  The theory of welded and extended welded knots is a generalization of
classical knot theory. Welded (resp. extended welded) knot diagrams include
virtual crossings (resp. virtual crossings and wen marks) and are equivalent
under an extended set of Reidemeister-type moves.
  We present a new class of invariants for welded and extended welded knots and
links using a multi-skein relation, following Z. Yang's approach for virtual
knots. Using this skein-theoretic approach, we find sufficient conditions on
the coefficients to obtain invariance under the extended Reidemeister moves
appropriate to welded and extended welded links.
