New weighted generalizations for differentiable exponentially convex mapping with application
The main aim of the present paper is to present a novel approach base on the exponentially convex function to broaden the utilization of celebrated Hermite-Hadamard type inequality. The proposed technique presents an auxiliary result of constructing the set of base functions and gives deformation eq...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020229/fulltext.html |
| _version_ | 1817988545822851072 |
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| author | Saima Rashid Rehana Ashraf Muhammad Aslam Noor Khalida Inayat Noor Yu-Ming Chu |
| author_facet | Saima Rashid Rehana Ashraf Muhammad Aslam Noor Khalida Inayat Noor Yu-Ming Chu |
| author_sort | Saima Rashid |
| collection | DOAJ |
| description | The main aim of the present paper is to present a novel approach base on the exponentially convex function to broaden the utilization of celebrated Hermite-Hadamard type inequality. The proposed technique presents an auxiliary result of constructing the set of base functions and gives deformation equations in a simple form. The auxiliary result in the convexity has provided a convenient way of establishing the convergence region of several novel results. The strategy is not limited to the small parameter, such as in the classical method. The numerical examples obtained by the proposed approach indicate that the approach is easy to implement and computationally very attractive. The implementation of this numerical scheme clearly exhibits its effectiveness, reliability, and easiness regarding the applications in error estimates for weighted mean, the integral formula, rth moments of a continuous random variable, application to weighted special means and in developing the variants by extraordinary choices of n and θ as well as its better approximation. |
| first_indexed | 2024-04-14T00:35:25Z |
| format | Article |
| id | doaj.art-f00d6f085de54e2eb59820e0b0ee59f0 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-14T00:35:25Z |
| publishDate | 2020-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-f00d6f085de54e2eb59820e0b0ee59f02022-12-22T02:22:24ZengAIMS PressAIMS Mathematics2473-69882020-04-01543525354610.3934/math.2020229New weighted generalizations for differentiable exponentially convex mapping with applicationSaima Rashid0Rehana Ashraf1Muhammad Aslam Noor2Khalida Inayat Noor3Yu-Ming Chu41 Department of Mathematics, Government College (GC) University, Faisalabad, Pakistan2 Abdus Salam School of Mathematical Sciences, Government College (GC) University Lahore, Lahore, Pakistan3 Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan3 Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan4 Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China 5 School of Mathematics and Statistics, Changsha University of Science & Technology, Changsha 413000, P. R. ChinaThe main aim of the present paper is to present a novel approach base on the exponentially convex function to broaden the utilization of celebrated Hermite-Hadamard type inequality. The proposed technique presents an auxiliary result of constructing the set of base functions and gives deformation equations in a simple form. The auxiliary result in the convexity has provided a convenient way of establishing the convergence region of several novel results. The strategy is not limited to the small parameter, such as in the classical method. The numerical examples obtained by the proposed approach indicate that the approach is easy to implement and computationally very attractive. The implementation of this numerical scheme clearly exhibits its effectiveness, reliability, and easiness regarding the applications in error estimates for weighted mean, the integral formula, rth moments of a continuous random variable, application to weighted special means and in developing the variants by extraordinary choices of n and θ as well as its better approximation.https://www.aimspress.com/article/10.3934/math.2020229/fulltext.htmlconvex functionexponentially convex functionhermite-hadamard inequalityrth momentsweighted means |
| spellingShingle | Saima Rashid Rehana Ashraf Muhammad Aslam Noor Khalida Inayat Noor Yu-Ming Chu New weighted generalizations for differentiable exponentially convex mapping with application AIMS Mathematics convex function exponentially convex function hermite-hadamard inequality rth moments weighted means |
| title | New weighted generalizations for differentiable exponentially convex mapping with application |
| title_full | New weighted generalizations for differentiable exponentially convex mapping with application |
| title_fullStr | New weighted generalizations for differentiable exponentially convex mapping with application |
| title_full_unstemmed | New weighted generalizations for differentiable exponentially convex mapping with application |
| title_short | New weighted generalizations for differentiable exponentially convex mapping with application |
| title_sort | new weighted generalizations for differentiable exponentially convex mapping with application |
| topic | convex function exponentially convex function hermite-hadamard inequality rth moments weighted means |
| url | https://www.aimspress.com/article/10.3934/math.2020229/fulltext.html |
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