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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 inequality. Further, we construct a new family of exponentially convexfunctions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.

logarithmic convexity ; divided difference ; n-convex function ; majorization ; Sherman’s inequality ; Green’s function ; Fink’s identity ; Čebyšev functional ; Grüss-type inequality ; Ostrowski-type inequality ; exponential convexity

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