Mutual bounds for Jensen-type operator inequalities related to higher order convexity
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The main objective of this article is to establish mutual bounds for the Jensen operator inequality related to convex functions of higher order. First we give several mutual bounds for the operator version of the Lah-Ribarič inequality which hold for a class of n-convex functions. By virtue of the established estimates, we then derive several mutual bounds for the Jensen operator inequality which are also related to n-convex functions.
KeywordsJensen operator inequality Lah-Ribarič operator inequality n-Convexity Mutual bounds
Mathematics Subject ClassificationPrimary 47A63 Secondary 26A51
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The research of the third author was supported by the Ministry of Education and Science of the Russian Federation (The Agreement No. 02.a03.21.0008.)
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