k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications
This article is aimed at studying novel generalizations of Hermite-Mercer-type inequalities within the Riemann-Liouville k-fractional integral operators by employing s-convex functions. Two new auxiliary results are derived to govern the novel fractional variants of Hadamard-Mercer-type inequalities...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/5566360 |
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| _version_ | 1832546059633557504 |
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| author | Saad Ihsan Butt Jamshed Nasir Shahid Qaisar Khadijah M. Abualnaja |
| author_facet | Saad Ihsan Butt Jamshed Nasir Shahid Qaisar Khadijah M. Abualnaja |
| author_sort | Saad Ihsan Butt |
| collection | DOAJ |
| description | This article is aimed at studying novel generalizations of Hermite-Mercer-type inequalities within the Riemann-Liouville k-fractional integral operators by employing s-convex functions. Two new auxiliary results are derived to govern the novel fractional variants of Hadamard-Mercer-type inequalities for differentiable mapping Ψ whose derivatives in the absolute values are convex. Moreover, the results also indicate new lemmas for Ψ′, Ψ′′, and Ψ′′′ and new bounds for the Hadamard-Mercer-type inequalities via the well-known Hölder’s inequality. As an application viewpoint, certain estimates in respect of special functions and special means of real numbers are also illustrated to demonstrate the applicability and effectiveness of the suggested scheme. |
| format | Article |
| id | doaj-art-597c58dfccf74dda9c8e9d7d537fe46d |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-597c58dfccf74dda9c8e9d7d537fe46d2025-02-03T07:23:54ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/55663605566360k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with ApplicationsSaad Ihsan Butt0Jamshed Nasir1Shahid Qaisar2Khadijah M. Abualnaja3COMSATS University Islamabad, Lahore Campus, PakistanVirtual University, PakistanCOMSATS University Islamabad, Sahiwal Campus, PakistanDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaThis article is aimed at studying novel generalizations of Hermite-Mercer-type inequalities within the Riemann-Liouville k-fractional integral operators by employing s-convex functions. Two new auxiliary results are derived to govern the novel fractional variants of Hadamard-Mercer-type inequalities for differentiable mapping Ψ whose derivatives in the absolute values are convex. Moreover, the results also indicate new lemmas for Ψ′, Ψ′′, and Ψ′′′ and new bounds for the Hadamard-Mercer-type inequalities via the well-known Hölder’s inequality. As an application viewpoint, certain estimates in respect of special functions and special means of real numbers are also illustrated to demonstrate the applicability and effectiveness of the suggested scheme.http://dx.doi.org/10.1155/2021/5566360 |
| spellingShingle | Saad Ihsan Butt Jamshed Nasir Shahid Qaisar Khadijah M. Abualnaja k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications Journal of Function Spaces |
| title | k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications |
| title_full | k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications |
| title_fullStr | k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications |
| title_full_unstemmed | k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications |
| title_short | k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications |
| title_sort | k fractional variants of hermite mercer type inequalities via s convexity with applications |
| url | http://dx.doi.org/10.1155/2021/5566360 |
| work_keys_str_mv | AT saadihsanbutt kfractionalvariantsofhermitemercertypeinequalitiesviasconvexitywithapplications AT jamshednasir kfractionalvariantsofhermitemercertypeinequalitiesviasconvexitywithapplications AT shahidqaisar kfractionalvariantsofhermitemercertypeinequalitiesviasconvexitywithapplications AT khadijahmabualnaja kfractionalvariantsofhermitemercertypeinequalitiesviasconvexitywithapplications |