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Weighted Hermite-Hadamard and Simpson type inequalities for double integrals. (English) Zbl 1483.26014

In this paper, the authors derive and prove a weighted identity for twice partially differenciable mapping. In addition, the derived identity was used to establish a weighted Hermite-Hadamard-type inequality for co-ordinated convex functions on \(\mathbb{R^2}\). Furthermore, some weighted generalizations of Hermite-Hadamard- and Simpson-type integral inequalities were established and well proved.

MSC:

26D07 Inequalities involving other types of functions
26D10 Inequalities involving derivatives and differential and integral operators
26D15 Inequalities for sums, series and integrals
26B15 Integration of real functions of several variables: length, area, volume
26B25 Convexity of real functions of several variables, generalizations
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