Milne and Hermite-Hadamard's type inequalities for strongly multiplicative convex function via multiplicative calculus
In this paper, we take into account the notion of strongly multiplicative convex function and derive integral inequalities of Hermite-Hadamard ($ H.H $) type for such a function in the frame of multiplicative calculus. We also develop integral inequalities of $ H.H $ type for product and quotient of...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241625 |
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| author | Muhammad Umar Saad Ihsan Butt Youngsoo Seol |
| author_facet | Muhammad Umar Saad Ihsan Butt Youngsoo Seol |
| author_sort | Muhammad Umar |
| collection | DOAJ |
| description | In this paper, we take into account the notion of strongly multiplicative convex function and derive integral inequalities of Hermite-Hadamard ($ H.H $) type for such a function in the frame of multiplicative calculus. We also develop integral inequalities of $ H.H $ type for product and quotient of strongly multiplicative convex and strongly multiplicative concave functions via multiplicative calculus. All the results of the theorems are verified graphically by taking into account some reasonable examples. Additionally, we establish the inequalities of the Milne type for strongly multiplicative convex functions. |
| format | Article |
| id | doaj-art-2eab22f5aed54bbc8732bdbe17434015 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-2eab22f5aed54bbc8732bdbe174340152025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912340903410810.3934/math.20241625Milne and Hermite-Hadamard's type inequalities for strongly multiplicative convex function via multiplicative calculusMuhammad Umar0Saad Ihsan Butt1Youngsoo Seol2Department of Mathematics, COMSATS University Islamabad, Lahore Campus, PakistanDepartment of Mathematics, COMSATS University Islamabad, Lahore Campus, PakistanDepartment of Mathematics, Dong-A University, Busan 49315, KoreaIn this paper, we take into account the notion of strongly multiplicative convex function and derive integral inequalities of Hermite-Hadamard ($ H.H $) type for such a function in the frame of multiplicative calculus. We also develop integral inequalities of $ H.H $ type for product and quotient of strongly multiplicative convex and strongly multiplicative concave functions via multiplicative calculus. All the results of the theorems are verified graphically by taking into account some reasonable examples. Additionally, we establish the inequalities of the Milne type for strongly multiplicative convex functions.https://www.aimspress.com/article/doi/10.3934/math.20241625convex functionmultiplicative convex functionstrongly multiplicative convex functionhermite-hadamard type inequalitymilne type inequality |
| spellingShingle | Muhammad Umar Saad Ihsan Butt Youngsoo Seol Milne and Hermite-Hadamard's type inequalities for strongly multiplicative convex function via multiplicative calculus AIMS Mathematics convex function multiplicative convex function strongly multiplicative convex function hermite-hadamard type inequality milne type inequality |
| title | Milne and Hermite-Hadamard's type inequalities for strongly multiplicative convex function via multiplicative calculus |
| title_full | Milne and Hermite-Hadamard's type inequalities for strongly multiplicative convex function via multiplicative calculus |
| title_fullStr | Milne and Hermite-Hadamard's type inequalities for strongly multiplicative convex function via multiplicative calculus |
| title_full_unstemmed | Milne and Hermite-Hadamard's type inequalities for strongly multiplicative convex function via multiplicative calculus |
| title_short | Milne and Hermite-Hadamard's type inequalities for strongly multiplicative convex function via multiplicative calculus |
| title_sort | milne and hermite hadamard s type inequalities for strongly multiplicative convex function via multiplicative calculus |
| topic | convex function multiplicative convex function strongly multiplicative convex function hermite-hadamard type inequality milne type inequality |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241625 |
| work_keys_str_mv | AT muhammadumar milneandhermitehadamardstypeinequalitiesforstronglymultiplicativeconvexfunctionviamultiplicativecalculus AT saadihsanbutt milneandhermitehadamardstypeinequalitiesforstronglymultiplicativeconvexfunctionviamultiplicativecalculus AT youngsooseol milneandhermitehadamardstypeinequalitiesforstronglymultiplicativeconvexfunctionviamultiplicativecalculus |