New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators
In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for diffe...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/4303727 |
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| author | Qiong Kang Saad Ihsan Butt Waqas Nazeer Mehroz Nadeem Jamshed Nasir Hong Yang |
| author_facet | Qiong Kang Saad Ihsan Butt Waqas Nazeer Mehroz Nadeem Jamshed Nasir Hong Yang |
| author_sort | Qiong Kang |
| collection | DOAJ |
| description | In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping ϒ whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions ϒ′, ϒ″, and ϒ‴ and formulate related inequalities for these differentiable functions using variants of Hölder’s inequality. |
| format | Article |
| id | doaj-art-9b9778b2777e4d26b3035eac8fa25b88 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9b9778b2777e4d26b3035eac8fa25b882025-02-03T01:04:09ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/43037274303727New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral OperatorsQiong Kang0Saad Ihsan Butt1Waqas Nazeer2Mehroz Nadeem3Jamshed Nasir4Hong Yang5School of Computer Science, Yangtze University, Jingzhou 434023, ChinaComsat University Islamabad, Lahore Campus, Islamabad, PakistanDepartment of Mathematics, Government College University, Lahore, PakistanComsat University Islamabad, Lahore Campus, Islamabad, PakistanComsat University Islamabad, Lahore Campus, Islamabad, PakistanSchool of Information Science and Engineering, Chengdu University, Chengdu 610106, ChinaIn this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping ϒ whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions ϒ′, ϒ″, and ϒ‴ and formulate related inequalities for these differentiable functions using variants of Hölder’s inequality.http://dx.doi.org/10.1155/2020/4303727 |
| spellingShingle | Qiong Kang Saad Ihsan Butt Waqas Nazeer Mehroz Nadeem Jamshed Nasir Hong Yang New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators Journal of Mathematics |
| title | New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators |
| title_full | New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators |
| title_fullStr | New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators |
| title_full_unstemmed | New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators |
| title_short | New Variant of Hermite–Jensen–Mercer Inequalities via Riemann–Liouville Fractional Integral Operators |
| title_sort | new variant of hermite jensen mercer inequalities via riemann liouville fractional integral operators |
| url | http://dx.doi.org/10.1155/2020/4303727 |
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