An extension of the Hermite-Hadamard inequality for a power of a convex function

• DOI: 10.1515/math-2022-0542
• Publication Date: 2023-02-01T06:39:08Z
• Authors: Yamin Sayyari; Mehdi Dehghanian; Choonkil Park; Siriluk Paokanta
• Keywords: 52a40; Geometry; 52a41; Evolutionary biology; Convex Functions; Matrix Inequalities and Geometric Means; Mathematical analysis; 01 natural sciences; Orthogonal Polynomials; Operator Inequalities; Convergence Analysis of Iterative Methods for Nonlinear Equations; 26d15; Convex function; power function; QA1-939; FOS: Mathematics; jensen’s inequality; 0101 mathematics; Biology; Hadamard transform; convex function; Numerical Analysis; Hermite polynomials; Extension (predicate logic); hermite-hadamard inequality; Applied Mathematics; Discrete mathematics; Computer science; Convergence Analysis; Programming language; Regular polygon; Combinatorics; Function (biology); 26d07; Physical Sciences; error function; Hermite-Hadamard Inequalities; Mathematics; Hypergeometric Functions

Abstract In this article, we obtain an extension of the classical Hermite-Hadamard inequality for convex functions (concave functions) extending it to the power functions

[

f

(

x

)

]

n

{[f\left(x)]}^{n}

. Some related inequalities are also introduced. By applying those results in analysis, we obtain new upper and lower bounds for the error function.