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

Multi-Skein Invariants for Welded and Extended Welded Knots and Links