On integral operator generated by a symmetric difference expression

Using the concept of the symmetric difference formula of the Dunkl operator, a new fractional integral iteration of symmetric Schur functions is constructed in the open unit disk. That will be referred to as the fractional Schur–Dunkl operator. When applying the fractional Schur–Dunkl operator to the normalized class of holomorphic functions in the open unit disk, we take it into consideration. Some geometric criteria for the convexity and starlikeness of the envisaged operator are investigated. Furthermore, we declare a series of requirements for the fractional Schur–Dunkl operator to be in the domains of Symmetric Piatetski–Shapiro. Using Mathematica 13.3, figures are shown for the proposed fractional Schur–Dunkl operator.