Ostrowski and Hermite-Hadamard type inequalities via (α−s) exponential type convex functions with applications
Integral inequalities involving exponential convexity are significant in both theoretical and applied mathematics. In this paper, we establish a new Hermite-Hadamard type inequality for the class of exponentially convex functions by using the concept of $ (\alpha-s) $ exponentially convex function....
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AIMS Press
2024-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241364?viewType=HTML |
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| author | Attazar Bakht Matloob Anwar |
| author_facet | Attazar Bakht Matloob Anwar |
| author_sort | Attazar Bakht |
| collection | DOAJ |
| description | Integral inequalities involving exponential convexity are significant in both theoretical and applied mathematics. In this paper, we establish a new Hermite-Hadamard type inequality for the class of exponentially convex functions by using the concept of $ (\alpha-s) $ exponentially convex function. Additionally, using the well-known Hermite-Hadamard and Ostrowski inequalities, we establish several new integral inequalities. These newly obtained results contain several well-known results as special cases. Finally, new estimations for the trapezoidal formula have been provided, illustrating the practical applications of the research. |
| format | Article |
| id | doaj-art-e3438cda9bca41c7a2862b8a4d4e3bbb |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj-art-e3438cda9bca41c7a2862b8a4d4e3bbb2025-08-20T01:54:23ZengAIMS PressAIMS Mathematics2473-69882024-09-01910281302814910.3934/math.20241364Ostrowski and Hermite-Hadamard type inequalities via (α−s) exponential type convex functions with applicationsAttazar Bakht 0Matloob Anwar1Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad, PakistanDepartment of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad, PakistanIntegral inequalities involving exponential convexity are significant in both theoretical and applied mathematics. In this paper, we establish a new Hermite-Hadamard type inequality for the class of exponentially convex functions by using the concept of $ (\alpha-s) $ exponentially convex function. Additionally, using the well-known Hermite-Hadamard and Ostrowski inequalities, we establish several new integral inequalities. These newly obtained results contain several well-known results as special cases. Finally, new estimations for the trapezoidal formula have been provided, illustrating the practical applications of the research.https://www.aimspress.com/article/doi/10.3934/math.20241364?viewType=HTMLconvex functionexponential type s-convexityhermite hadamard inequalityostrowski inequalityholder's inequality |
| spellingShingle | Attazar Bakht Matloob Anwar Ostrowski and Hermite-Hadamard type inequalities via (α−s) exponential type convex functions with applications AIMS Mathematics convex function exponential type s-convexity hermite hadamard inequality ostrowski inequality holder's inequality |
| title | Ostrowski and Hermite-Hadamard type inequalities via (α−s) exponential type convex functions with applications |
| title_full | Ostrowski and Hermite-Hadamard type inequalities via (α−s) exponential type convex functions with applications |
| title_fullStr | Ostrowski and Hermite-Hadamard type inequalities via (α−s) exponential type convex functions with applications |
| title_full_unstemmed | Ostrowski and Hermite-Hadamard type inequalities via (α−s) exponential type convex functions with applications |
| title_short | Ostrowski and Hermite-Hadamard type inequalities via (α−s) exponential type convex functions with applications |
| title_sort | ostrowski and hermite hadamard type inequalities via α s exponential type convex functions with applications |
| topic | convex function exponential type s-convexity hermite hadamard inequality ostrowski inequality holder's inequality |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241364?viewType=HTML |
| work_keys_str_mv | AT attazarbakht ostrowskiandhermitehadamardtypeinequalitiesviaasexponentialtypeconvexfunctionswithapplications AT matloobanwar ostrowskiandhermitehadamardtypeinequalitiesviaasexponentialtypeconvexfunctionswithapplications |