New Class of Generalized Hermite-Hadamard Type Inequalities

Travail de Recherche , 2024 , 39 Pages

Mathématiques - Analyse

The graphical elegance of fractal theory takes into account the development's achievability and exceptionalism. Due to its fascinating existence in the mathematical fields of sciences, there is a clear association between fractal sets and convexity. In this proposal, we will present generalized convexity and related integral inequalities on a fractal set Rϖ ( 0 < ϖ ≤ 1). In the context of the Beta function, this research presents a new class of generalized Hermite-Hadamard type inequalities.

This research contributes significant results of novel versions of fractal Hölder's and Young's inequalities. We derive some general conclusions that capture novel results under investigation. One more remarkable contribution of the study is that two novel auxiliary results along with Trapezoidal and Midpoint type inequalities are provided. Hence, these new results will lead us to generalization of prior results.

TABLE OF CONTENTS

1 Preliminaries And Introduction
1.1 Convex Functions
1.2 Special functions
1.3 Local Fractional Calculus on Rϖ
1.4 Generalized Convex Function
1.5 Generalized Special Functions

2 Back Ground Of The Problem
2.1 Hermite–Hadamard Inequality
2.2 Jensen-Mercer Inequality
2.3 Generalized Hermite–Hadamard’s Inequality
2.4 Generalized Jensen-Mercer Inequality
2.5 Generalized H¨older’s Inequality
2.6 Generalized Young’s Inequality

3 Main Results
3.1 Result’s for Fractal Trapezoid Inequalities
3.2 Result’s for Fractal Midpoint Inequalities
3.3 Result’s for Fractal Trapezoidal Inequalities in Mercer sense
3.4 Result’s for Fractal Midpoint Inequalities in Mercer sense

4 Conclusion

• Auteur: Iram Javed (Auteur)
• Année de publication: 2024
• Pages: 39
• N° de catalogue: V1442888
• ISBN (PDF): 9783964877062
• ISBN (Livre): 9783964877079
• Langue: allemand
• mots-clé: class, generalized, hermite-hadamard, type, inequalities