Hermite-Hadamard type inequalities for F-convex function involving fractional integrals

Area of Science:

• Mathematical Analysis
• Convexity Theory
• Fractional Calculus

Background:

• The study builds upon existing Hermite-Hadamard and trapezoid inequalities.
• It introduces the concept of F-convex functions and their properties.

Purpose of the Study:

• To define and explore the properties of F-convex functions.
• To establish new Hermite-Hadamard type inequalities for differentiable functions.
• To derive new trapezoid type inequalities using F-convex functions and fractional integrals.

Main Methods:

• Introduction of the F-convex function family.
• Application of F-convexity to establish Hermite-Hadamard inequalities.
• Development of trapezoid inequalities for functions with F-convex second derivatives.
• Extension of inequalities to Riemann-Liouville fractional integrals.

Main Results:

• New inequalities of Hermite-Hadamard type for differentiable functions are established.
• New trapezoid type inequalities are derived for functions whose second derivatives are F-convex.
• The F-convexity notion is utilized to formulate novel inequalities for fractional integrals.

Conclusions:

• The concept of F-convex functions provides a framework for new integral inequalities.
• The study extends classical inequalities to fractional calculus settings.
• The findings contribute to the theory of inequalities and fractional analysis.