DEFINITION, EXISTENCE, NEGATIVITY, AND INTEGRAL INEQUALITIES OF HERMITE–HADAMARD TYPE FOR MTH-CONVEX FUNCTIONS

Shu-Ping Bai; Feng Qi

doi:10.11948/20260262

2027 Volume 17 Issue 2

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Shu-Ping Bai, Feng Qi. DEFINITION, EXISTENCE, NEGATIVITY, AND INTEGRAL INEQUALITIES OF HERMITE–HADAMARD TYPE FOR MTH-CONVEX FUNCTIONS[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 1611-1622. doi: 10.11948/20260262

Citation:

Shu-Ping Bai, Feng Qi. DEFINITION, EXISTENCE, NEGATIVITY, AND INTEGRAL INEQUALITIES OF HERMITE–HADAMARD TYPE FOR MTH-CONVEX FUNCTIONS[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 1611-1622. doi: 10.11948/20260262

DEFINITION, EXISTENCE, NEGATIVITY, AND INTEGRAL INEQUALITIES OF HERMITE–HADAMARD TYPE FOR MTH-CONVEX FUNCTIONS

Shu-Ping Bai^1,,
Feng Qi^2,3, ,

1.
College of Mathematical Sciences, Inner Mongolia Minzu University, Tongliao 028043, Inner Mongolia, China
2.
School of Mathematics and Physics, Hulunbuir University, Hulunbuir 021008, Inner Mongolia, China
3.
17709 Sabal Court, University Village, Dallas, TX 75252-8024, USA

Author Bio: E-mail: bsp0838@126.com(S.-P. Bai)
Corresponding author: E-mail: qifeng618@gmail.com(F. Qi)

Abstract

Abstract

In the paper, the authors introduce a concept of MTH-convex functions, provide an illustrative example of the MTH-convex functions, prove that every MTH-convex function is negative, and establish several new integral inequalities of the Hermite–Hadamard type for this class of functions.
- MTH-convex function /
- property /
- example /
- convex function /
- integral inequality /
- Hermite-Hadamard type
MSC: 26A51, 26D15, 26E60, 41A55

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References

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