New General Integral Inequalities for Polynomial Convexity in the Framework of k-Riemann–Liouville Fractional Operators

The Hermite–Hadamard inequality, which is widely recognized and studied in the field of inequalities, and the k-Riemann–Liouville fractional integral inequality, which is a generalization of the Riemann–Liouville fractional operator in operator theory, play a significant role in the existing literature concerning the concept of inequality. Along with the definitions, theorems, and inequalities already in the literature, new generalizations have been created based on the properties of the convex function discussed in this article, which are called n-polynomial ς-convex functions. Hölder, power mean, and Young inequalities have been utilized to derive these significant results. Consequently, it is hypothesized that the new theorems obtained in this paper will serve as a guide for future work in this area.