This paper provides some characteristic properties of the weighted particular Schur polynomial mean of several variables. In addition, an elementary proof of an important inequality involving the weighted particular Schur polynomial mean is given. Various related results involving a family of the Schur polynomials, symmetric polynomials, and other associated polynomials, together with the potential for their applications, are also considered.
KEYWORDSelementary proofs, inequalities and characteristic properties, particular Schur polynomial, Schur polynomial, weighted particular Schur polynomial mean MSC CLASSIFICATION Primary 15A42; 26D15; Secondary 26D07; 26E40 Math Meth Appl Sci. 2019;42:6459-6474. wileyonlinelibrary.com/journal/mma