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Hermite-Hadamard inequalities and their applications.

Marcela V Mihai¹, Muhammad Uzair Awan², Muhammad Aslam Noor³

¹Department Scientific-Methodical Sessions, Romanian Mathematical Society-Branch Bucharest, Bucharest, Romania.

Journal of Inequalities and Applications

|March 7, 2019

Summary

New Hermite-Hadamard inequalities were established, offering novel mathematical insights. Detailed examples illustrate the application and significance of these findings in mathematical analysis.

Keywords:

Generalized logarithmic means Hermite–Hadamard inequalities log-convex function

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Area of Science:

Mathematical Analysis
Inequalities Theory

Background:

The Hermite-Hadamard inequality is a fundamental result in convex analysis.
Existing inequalities provide bounds for integral properties of convex functions.

Purpose of the Study:

To establish new variants of the Hermite-Hadamard type inequalities.
To extend the existing body of knowledge in inequality theory.

Main Methods:

Utilizing techniques from classical analysis.
Developing novel mathematical derivations for inequality proofs.

Main Results:

The paper introduces and proves several new Hermite-Hadamard type inequalities.
The established inequalities offer tighter or more generalized bounds compared to previous results.

Conclusions:

The newly established inequalities contribute to the field of mathematical analysis.
The detailed examples demonstrate the practical relevance and applicability of the new findings.