engleski

Generalization of Cyclic Refinements of Jensen Inequality by Fink's Identity

We generalize cyclic refinements of Jensen’s inequality from a convex function to a higher-order convex function by means of Lagrange–Green’s function and Fink’s identity. We formulate the monotonicity of the linear functionals obtained from these identities utilizing the theory of inequalities for n-convex functions at a point. New Grüss- and Ostrowski-type bounds are found for identities associated with the obtained inequalities. Finally, we investigate the properties of linear functionals regarding exponential convexity and mean value theorems.

Convex function ; n-Convex function at a point ; Fink’s identity ; Green function ; Cebyšev functional ; Grüss and Ostrowski inequality

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