The best interval quadrature formula is obtained for the class of convex set-valued functions defined on the segment [0, 1] and monotone with respect to inclusion.
Similar content being viewed by others
References
J. Kiefer, “Optimum sequential search and approximation methods under minimum regularity assumptions,” J. Soc. Indust. Appl. Math., 5, No. 3, 105–136 (1957).
V. F. Babenko and S. V. Borodachev, “On optimization of cubature monotone functions of several variables,” Visn. Dnipropetr. Univ., Ser. Mat., Issue 7, 3–7 (2002).
V. B. Babenko and V. V. Babenko, “Optimization of approximate integration of set-valued functions monotone with respect to inclusion,” Ukr. Mat. Zh., 63, No. 2, 147–155 (2011); English translation: Ukr. Math. J., 63, No. 2, 177–186 (2011).
M. Hukuhara, “Intégration des applications mesurables dont la valeur est un compact convexe,” Funkc. Ekvac., 10, 205–223 (1967).
N. P. Korneichuk, Extremal Problems in Approximation Theory [in Russian], Nauka, Moscow (1976).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 11, pp. 1565–1569, November, 2011.
Rights and permissions
About this article
Cite this article
Babenko, V.V. Optimization of interval formulas for approximate integration of set-valued functions monotone with respect to inclusion. Ukr Math J 63, 1781–1786 (2012). https://doi.org/10.1007/s11253-012-0613-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-012-0613-5