Refinements of the majorization-type inequalities via green and fink identities and related results

• Published in: Mathematica Slovaca Vol. 68; no. 4; pp. 773 - 788
• Main Authors: Khalid, Sadia, Pečarić, Josip, Vukelić, Ana
• Format: Journal Article
• Language: English
• Published: Heidelberg De Gruyter 28.08.2018; Walter de Gruyter GmbH
• Subjects: 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

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...