Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex

Abstract

In this paper, we extend some estimates of a Hermite-Hadamard type inequality for functions whose absolute values of the first derivatives are $p$-convex. By means of the obtained inequalities, some bound functions involving beta functions and hypergeometric functions are derived as applications. Also, we suggest an upper bound for error in numerical integration of $p$-convex functions via composite trapezoid rule.

Keywords

• Hermite-Hadamard inequality
• $p$-convex function
• Convexity

References

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