Hermite-Hadamard Inequalities for a New Class of Generalized-(s,m) via Fractional Integral

Abstract

This paper defines a new generalized (s,m)-σ convex function using the σ convex functions and provides some applications and exact results for this kind of functions. The new definition of the (s,m)-σ convex function class is used to obtain the Hermite Hadamard type integral inequalities existing in the literature, and new integral inequalities are obtained with the help of the σ-Riemann-Liouville fractional integral. Additionally, a new Hermite-Hadamard type fractional integral inequality is constructed using the σ-Riemann-Liouville fractional integral.

Keywords

• Hermite–Hadamard inequality
• fractional İntegral operator
• Convex function
• σ-convex function
• (s-m)-σ convex function.

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