Certain multiple integral relations involving multivariable $ H $-function and general polynomials

In this paper, first we obtain a finite integral involving multivariable $ H $-function and general classes of polynomials. Next, with the application of this and a lemma due to Srivastava et al. (1981) we obtain two general multiple integral relations involving the multivariable $ H $-function, general classes of polynomials and two arbitrary function $ f $ and $ g $. Again, by suitably specializing the functions $ f $ and $ g $ occurring in the main integral relations, we have also evaluated multiple integrals which are new and quite general in nature.