Before revision:  In this article  , we  take a closer look at  various existing mapped WENO schemes in references to obtain a general formula for their mapping functions that allows the extension of the OP criterion to all existing mapped WENO schemes . The improved mapped WENO scheme considerring the OP criterion based on the existing mapped WENO-X schemeis named ] ] ] ] MOP-WENO-X.
After revision:  In this article , we take a closer look at various existing mapped WENO schemes in references to obtain a general formula for them. It helps us to extend the order-preserving (OP) criterion, originally defined and carefully examined in ] ] ] ] MOP-WENO-X.