Some generalizations of the Hermite–Hadamard integral inequality

Simić, Slavko; Bin‐Mohsin, Bandar

doi:10.1186/s13660-021-02605-y

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2022

2024

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Cited by 2 publications

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“…It has many applications in different areas of pure and applied mathematics. For some references about this latter point, we can consult [1][2][3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Refined Hermite–Hadamard Inequalities and Some Norm Inequalities

Yanagi

2022

Symmetry

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It is well known that the Hermite–Hadamard inequality (called the HH inequality) refines the definition of convexity of function f(x) defined on [a,b] by using the integral of f(x) from a to b. There are many generalizations or refinements of HH inequality. Furthermore HH inequality has many applications to several fields of mathematics, including numerical analysis, functional analysis, and operator inequality. Recently, we gave several types of refined HH inequalities and obtained inequalities which were satisfied by weighted logarithmic means. In this article, we give an N-variable Hermite–Hadamard inequality and apply to some norm inequalities under certain conditions. As applications, we obtain several inequalities which are satisfied by means defined by symmetry. Finally, we obtain detailed integral values.

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“…It has many applications in different areas of pure and applied mathematics. For some references about this latter point, we can consult [1][2][3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%