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

Feixiang Chen1, Shanhe Wu2

  • 1School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing 404000, China.

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Summary

This study provides new estimates for Hermite-Hadamard type inequalities involving functions with harmonically s-convex derivatives. It also explores these inequalities for products of two such functions.

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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.