Integral inequalities of Hermite-Hadamard type for quasi-convex functions with applications

Pshtiwan Othman Mohammed; Miguel Vivas-Cortez; Thabet Abdeljawad; Yenny Rangel-Oliveros; Pshtiwan Othman Mohammed; Miguel Vivas-Cortez; Thabet Abdeljawad; Yenny Rangel-Oliveros

doi:10.3934/math.2020468

AIMS Mathematics

2020, Volume 5, Issue 6: 7316-7331. doi: 10.3934/math.2020468

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Research article

Integral inequalities of Hermite-Hadamard type for quasi-convex functions with applications

1.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq
2.
Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Av. 12 de Octubre 1076. Apartado, Quito 17-01-2184, Ecuador
3.
Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
5.
Department of Computer Science and Information Engineering, Asia University, Taichung 41354, Taiwan

Received: 13 July 2020 Accepted: 16 September 2020 Published: 18 September 2020
MSC : 26A33, 39A12, 49K05

There is a strong connection between convexity and inequalities. So, techniques from each concept applies to the other due to the strong correlation between them; specifically, in the past few years. In this attempt, we consider the Hermite-Hadamard inequality and related inequalities for the class of functions whose absolute value of the third derivative are quasi-convex functions. Finally, the applications of our findings for special functions and particular functions are pointed out.
- Hermite-Hadamard inequality,
- quasi-convex function,
- Hölder inequality
Citation: Pshtiwan Othman Mohammed, Miguel Vivas-Cortez, Thabet Abdeljawad, Yenny Rangel-Oliveros. Integral inequalities of Hermite-Hadamard type for quasi-convex functions with applications[J]. AIMS Mathematics, 2020, 5(6): 7316-7331. doi: 10.3934/math.2020468

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Abstract

There is a strong connection between convexity and inequalities. So, techniques from each concept applies to the other due to the strong correlation between them; specifically, in the past few years. In this attempt, we consider the Hermite-Hadamard inequality and related inequalities for the class of functions whose absolute value of the third derivative are quasi-convex functions. Finally, the applications of our findings for special functions and particular functions are pointed out.

References

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