Mathematical Methods and Modelling in Applied Sciences by Mehmet Zeki Sarıkaya & Hemen Dutta & Ahmet Ocak Akdemir & Hari M. Srivastava

Author:Mehmet Zeki Sarıkaya & Hemen Dutta & Ahmet Ocak Akdemir & Hari M. Srivastava
Language: eng
Format: epub
ISBN: 9783030430023
Publisher: Springer International Publishing

Fig. 2.Surface in the three-dimensional space

The following is the effect of Theorem 1 to surface arches in .

Corollary 3

Let be a parametric surface arch in the space , let be a nonnegative integrable function with a positive integral, let be integrable functions, let be a tetrahedron containing the image of the mapping , and let be the convex combination such that

(24)

Then each convex function satisfies the double inequality

(25)

Proof

It fits in the proof of Corollary 1 if we employ the set D instead of the interval I, and if we use the function designated by

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