Generalized Steffensen’s inequality by Montgomery identity
Abstract By using generalized Montgomery identity and Green functions we proved several identities which assist in developing connections with Steffensen’s inequality. Under the assumptions of n-convexity and n-concavity many inequalities, which generalize Steffensen’s inequality, inequalities from...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-07-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2147-y |
| _version_ | 1811223427257729024 |
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| author | Saad Ihsan Butt Asfand Fahad Adil Naseer Josip Pečarić |
| author_facet | Saad Ihsan Butt Asfand Fahad Adil Naseer Josip Pečarić |
| author_sort | Saad Ihsan Butt |
| collection | DOAJ |
| description | Abstract By using generalized Montgomery identity and Green functions we proved several identities which assist in developing connections with Steffensen’s inequality. Under the assumptions of n-convexity and n-concavity many inequalities, which generalize Steffensen’s inequality, inequalities from (Fahad et al. in J. Math. Inequal. 9:481–487, 2015; Pečarić in Southeast Asian Bull. Math. 13:89–91, 1989; Rabier in Proc. Am. Math. Soc. 140:665–675, 2012), and their reverse, have been proved. Generalization of some inequalities (and their reverse) which are related to Hardy-type inequality (Fahad et al. in J. Math. Inequal. 9:481–487, 2015) have also been proved. New bounds of Ostrowski and Grüss type inequalities have been developed. Moreover, we formulate generalized Steffensen-type linear functionals and prove their monotonicity for the generalized class of (n+1) $(n+1)$-convex functions at a point. At the end, we present some applications of our study to the theory of exponentially convex functions. |
| first_indexed | 2024-04-12T08:32:47Z |
| format | Article |
| id | doaj.art-3d771a022aea462f855355487bad69df |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-12T08:32:47Z |
| publishDate | 2019-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-3d771a022aea462f855355487bad69df2022-12-22T03:40:07ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-07-012019112310.1186/s13660-019-2147-yGeneralized Steffensen’s inequality by Montgomery identitySaad Ihsan Butt0Asfand Fahad1Adil Naseer2Josip Pečarić3Department of Mathematics, COMSATS University IslamabadDepartment of Mathematics, COMSATS University IslamabadDepartment of Mathematics, COMSATS University IslamabadRUDN UniversityAbstract By using generalized Montgomery identity and Green functions we proved several identities which assist in developing connections with Steffensen’s inequality. Under the assumptions of n-convexity and n-concavity many inequalities, which generalize Steffensen’s inequality, inequalities from (Fahad et al. in J. Math. Inequal. 9:481–487, 2015; Pečarić in Southeast Asian Bull. Math. 13:89–91, 1989; Rabier in Proc. Am. Math. Soc. 140:665–675, 2012), and their reverse, have been proved. Generalization of some inequalities (and their reverse) which are related to Hardy-type inequality (Fahad et al. in J. Math. Inequal. 9:481–487, 2015) have also been proved. New bounds of Ostrowski and Grüss type inequalities have been developed. Moreover, we formulate generalized Steffensen-type linear functionals and prove their monotonicity for the generalized class of (n+1) $(n+1)$-convex functions at a point. At the end, we present some applications of our study to the theory of exponentially convex functions.http://link.springer.com/article/10.1186/s13660-019-2147-ySteffensen’s inequalityGreen’s functionMontgomery’s identity( n + 1 ) $(n+1)$ -convex function at a point |
| spellingShingle | Saad Ihsan Butt Asfand Fahad Adil Naseer Josip Pečarić Generalized Steffensen’s inequality by Montgomery identity Journal of Inequalities and Applications Steffensen’s inequality Green’s function Montgomery’s identity ( n + 1 ) $(n+1)$ -convex function at a point |
| title | Generalized Steffensen’s inequality by Montgomery identity |
| title_full | Generalized Steffensen’s inequality by Montgomery identity |
| title_fullStr | Generalized Steffensen’s inequality by Montgomery identity |
| title_full_unstemmed | Generalized Steffensen’s inequality by Montgomery identity |
| title_short | Generalized Steffensen’s inequality by Montgomery identity |
| title_sort | generalized steffensen s inequality by montgomery identity |
| topic | Steffensen’s inequality Green’s function Montgomery’s identity ( n + 1 ) $(n+1)$ -convex function at a point |
| url | http://link.springer.com/article/10.1186/s13660-019-2147-y |
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