Some Hermite-Hadamard type inequalities for harmonically s-convex functions

Area of Science:

• Mathematical Analysis
• Convexity Theory

Background:

• Hermite-Hadamard inequalities are fundamental in convex analysis.
• Harmonically s-convex functions represent a generalization of convex functions.

Purpose of the Study:

• To establish new estimates for the right-hand side of Hermite-Hadamard type inequalities.
• To investigate these inequalities for functions with harmonically s-convex derivatives.
• To extend the analysis to products of two harmonically s-convex functions.

Main Methods:

• Utilizing definitions and properties of harmonically s-convex functions.
• Applying analytical techniques to derive inequality estimates.
• Developing new inequalities based on function derivatives.

Main Results:

• New estimates for Hermite-Hadamard type inequalities were established.
• Inequalities were derived for functions whose derivatives' absolute values are harmonically s-convex.
• Results were extended to the product of two harmonically s-convex functions.

Conclusions:

• The study contributes novel results to the field of convex analysis and inequalities.
• The findings offer new tools for analyzing functions with specific convexity properties.