Refinements of the majorization-type inequalities via green and fink identities and related results
In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type in...
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| Published in | Mathematica Slovaca Vol. 68; no. 4; pp. 773 - 788 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
De Gruyter
28.08.2018
Walter de Gruyter GmbH |
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| Abstract | In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities. |
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| AbstractList | In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities. |
| Author | Pečarić, Josip Khalid, Sadia Vukelić, Ana |
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| SubjectTerms | 26D15 convex function divided difference exponential convexity Fink’s identity Functionals Green’s function Grüss-type inequality Inequalities Inequality logarithmic convexity majorization Ostrowski-type inequality Primary 26A51 Sherman’s inequality Čebyšev functional |
| Title | Refinements of the majorization-type inequalities via green and fink identities and related results |
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