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Research Article | Open Access

On some Simpson's and Newton's type of inequalities in multiplicative calculus with applications

Saowaluck Chasreechai1, Muhammad Aamir Ali2, Surapol Naowarat3, Thanin Sitthiwirattham4, Kamsing Nonlaopon5( )
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China
Department of Mathematics, Faculty of Science and Technology, Suratthani Rajabhat University, Surat Thani 84100, Thailand
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
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Abstract

In this paper, we establish an integral equality involving a multiplicative differentiable function for the multiplicative integral. Then, we use the newly established equality to prove some new Simpson's and Newton's inequalities for multiplicative differentiable functions. Finally, we give some mathematical examples to show the validation of newly established inequalities.

Keywords

Simpson's inequalitiesNewton's inequalitiesconvex functionsmultiplicative calculus
CLC number: 26D07, 26D10, 26D15

References

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AIMS Mathematics
Volume 8 Issue 2,
February 2023
Pages 3885-3896
DOI: 10.3934/math.2023193

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Cite this article:
Chasreechai S, Ali MA, Naowarat S, et al. On some Simpson's and Newton's type of inequalities in multiplicative calculus with applications. AIMS Mathematics, 2023, 8(2): 3885-3896. https://doi.org/10.3934/math.2023193

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Received: 04 October 2022
Revised: 04 November 2022
Accepted: 09 November 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)