$ (m, n) $-Harmonically polynomial convex functions and some Hadamard type inequalities on the co-ordinates

Saad Ihsan Butt; Ahmet Ocak Akdemir; Muhammad Nadeem; Nabil Mlaiki; İşcan İmdat; Thabet Abdeljawad; Saad Ihsan Butt; Ahmet Ocak Akdemir; Muhammad Nadeem; Nabil Mlaiki; İşcan İmdat; Thabet Abdeljawad

doi:10.3934/math.2021275

AIMS Mathematics

2021, Volume 6, Issue 5: 4677-4690. doi: 10.3934/math.2021275

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Research article

$ (m, n) $-Harmonically polynomial convex functions and some Hadamard type inequalities on the co-ordinates

1.
COMSATS University Islamabad, Lahore Campus, Pakistan
2.
Ağrı İbrahim Çeçen University, Faculty of Science and Arts, Department of Mathematics, 04100, Ağrı, Turkey
3.
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
4.
Giresun University, Faculty of Science and Arts, Department of Mathematics, Giresun, Turkey
5.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
6.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

Received: 12 December 2020 Accepted: 18 February 2021 Published: 24 February 2021
MSC : 26D10, 26D15

In this study, we have introduced a new concept called $ (m, n) $-harmonically polynomial convex functions on the co-ordinates. Then, we have demonstrated some properties of this definition. Based on the definition and some elementary analysis process, we have proved a new Hadamard type integral inequality on the coordinates for $ (m, n) $-harmonically polynomial convex functions. Finally, we have established Hadamard type inequality for differentiable $ (m, n) $-Harmonically polynomial convex functions. We have also given some special cases for bounded functions.
- Hadamard-type inequality,
- co-ordinates,
- $ (m, n) $-harmonically polynomial convex functions
Citation: Saad Ihsan Butt, Ahmet Ocak Akdemir, Muhammad Nadeem, Nabil Mlaiki, İşcan İmdat, Thabet Abdeljawad. $ (m, n) $-Harmonically polynomial convex functions and some Hadamard type inequalities on the co-ordinates[J]. AIMS Mathematics, 2021, 6(5): 4677-4690. doi: 10.3934/math.2021275

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Abstract

In this study, we have introduced a new concept called $ (m, n) $-harmonically polynomial convex functions on the co-ordinates. Then, we have demonstrated some properties of this definition. Based on the definition and some elementary analysis process, we have proved a new Hadamard type integral inequality on the coordinates for $ (m, n) $-harmonically polynomial convex functions. Finally, we have established Hadamard type inequality for differentiable $ (m, n) $-Harmonically polynomial convex functions. We have also given some special cases for bounded functions.

References

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