Improved Bounds of Hermite Hadamard Inequality for Several Kinds of Convexities via Fractional Integral

This research work deals with generalizations and refinements of bounds of the first inequality of the celebrated Hermite Hadamard dual inequality via Riemann-Liouville fractional integrals. Specifically, we explore generalized integral inequalities for several kinds of convexities using fractional integrals by utilizing the newly defined class of (s_۱, s_۲, t_۱, t_۲)-convex functions. The proposed research work establishes the superiority of an enhanced version of the power-mean integral inequality and H\"{o}lder integral inequality, termed as improved power-mean and H\"{o}lder-\.{I}\c{s}can integral inequalities, over the traditional ones.

کلیدواژه ها:

Hermite Hadamard inequality ، Riemann-Liouville fractional integrals ، Convex functions ، (s۱ ، s۲ ، t۱ ، t۲)-convexity ، Improved power-mean inequality ، Holder-Iscan integral inequality