Novel Mean-Type Inequalities via Generalized Riemann-Type Fractional Integral for Composite Convex Functions: Some Special Examples

This study deals with a novel class of mean-type inequalities by employing fractional calculus and convexity theory. The high correlation between symmetry and convexity increases its significance. In this paper, we first establish an identity that is crucial in investigating fractional mean inequalities. Then, we establish the main results involving the error estimation of the Hermite-Hadamard inequality for composite convex functions via a generalized Riemann-type fractional integral. Such results are verified by choosing certain composite functions. These results give well-known examples in special cases. The main consequences can generalize many known inequalities that exist in other studies.

Automated summary

This study introduces a new class of mean-type inequalities using fractional calculus and convexity theory. The strong correlation between symmetry and convexity increases its significance. The study establishes a crucial identity for investigating fractional mean inequalities and provides main results related to the error estimation of the Hermite-Hadamard inequality for composite convex functions through a generalized Riemann-type fractional integral. These results are verified in specific cases and have the potential to extend known inequalities from other studies.