On inequalities of Hermite-Hadamard type via $ n $-polynomial exponential type $ s $-convex functions

Muhammad Samraiz; Kanwal Saeed; Saima Naheed; Gauhar Rahman; Kamsing Nonlaopon; Muhammad Samraiz; Kanwal Saeed; Saima Naheed; Gauhar Rahman; Kamsing Nonlaopon

doi:10.3934/math.2022787

AIMS Mathematics

2022, Volume 7, Issue 8: 14282-14298. doi: 10.3934/math.2022787

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Research article

On inequalities of Hermite-Hadamard type via $ n $-polynomial exponential type $ s $-convex functions

1.
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
2.
Department of Mathematics and Statistics Hazara University Mansehra, Pakistan
3.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 18 February 2022 Revised: 30 April 2022 Accepted: 12 May 2022 Published: 01 June 2022
MSC : 26D15, 26D10, 26A33, 34B27

In this paper, a new class of Hermite-Hadamard type integral inequalities using a strong type of convexity, known as $ n $-polynomial exponential type $ s $-convex function, is studied. This class is established by utilizing the Hölder's inequality, which has several applications in optimization theory. Some existing results of the literature are obtained from newly explored consequences. Finally, some novel limits for specific means of positive real numbers are shown as applications.
- Hermite-Hadamard's type inequalities,
- $ n $-polynomial exponential convex functions,
- $ s $-convex function,
- special means,
- Hölder's inequality
Citation: Muhammad Samraiz, Kanwal Saeed, Saima Naheed, Gauhar Rahman, Kamsing Nonlaopon. On inequalities of Hermite-Hadamard type via $ n $-polynomial exponential type $ s $-convex functions[J]. AIMS Mathematics, 2022, 7(8): 14282-14298. doi: 10.3934/math.2022787

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Abstract

In this paper, a new class of Hermite-Hadamard type integral inequalities using a strong type of convexity, known as $ n $-polynomial exponential type $ s $-convex function, is studied. This class is established by utilizing the Hölder's inequality, which has several applications in optimization theory. Some existing results of the literature are obtained from newly explored consequences. Finally, some novel limits for specific means of positive real numbers are shown as applications.

References

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