engleski

General Opial type inequality

In this paper our goal is to give general Opial type inequality. We consider two functions, convex and concave and prove a new general inequality on a measure space. The obtained inequalities are not direct generalizations of the Opial inequality but are of Opial type because the integrals contain function and its integral representation. We apply our result to numerous symmetric functions and obtain new results that involve Green's functions, Lindstone series and the Hermite's interpolating polynomials.

Opial inequality; Green function; Jensen inequality; Lidstone polynomial; Hermite interpolating polynomial

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