Extensions of Hermite - Hadamard Inequalities for Semi-P-Functions
DOI:
https://doi.org/10.55544/jrasb.5.5.2Keywords:
Hermite–Hadamard inequality, semi P-functions, extended Hermite–Hadamard inequality, Hölder’s inequality, power mean inequality, integral inequalities, meansAbstract
In this paper, several extended Hermite–Hadamard type inequalities are established for semi P-functions. By employing the extended Hermite–Hadamard inequality, new integral estimates are derived under the semi P-convexity framework. In addition, Hölder’s inequality and the power mean inequality are applied to obtain further bounds and refinements for the corresponding integral expressions. Some of the obtained results provide extensions and generalizations of existing Hermite–Hadamard type inequalities for semi P-functions. Furthermore, applications of the obtained inequalities to several classical means are presented, illustrating their usefulness in establishing relationships and bounds among different means. The results demonstrate that the semi P-function framework, together with Hölder’s inequality and the power mean inequality, provides a flexible approach for deriving refined integral inequalities and their applications.
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