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Some inequalities of Jensen’s type for Lipschitzian maps between Banach spaces. (English) Zbl 06946363

Summary: In this article, we consider some Jensen-type inequalities for Lipschitzian maps between Banach spaces and functions defined by power series. We obtain as applications some inequalities of Levinson type for Lipschitzian maps. Applications for functions of norms in Banach spaces are provided as well.

MSC:

47A63 Linear operator inequalities
47A99 General theory of linear operators
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References:

[1] H. Araki and S. Yamagami, An inequality for Hilbert-Schmidt norm, Comm. Math. Phys. 81 (1981), no. 1, 89–96. · Zbl 0468.47013 · doi:10.1007/BF01941801
[2] R. Bhatia, Perturbation bounds for the operator absolute value, Linear Algebra Appl. 226/228 (1995), 639–645. · Zbl 0835.47009 · doi:10.1016/0024-3795(95)00201-2
[3] S. S. Chang, Y. Q. Chen, and B. S. Lee, On the semi-inner products in locally convex spaces, Int. J. Math. Math. Sci. 20 (1997), no. 2, 219–224. · Zbl 0899.46015 · doi:10.1155/S0161171297000288
[4] Y. J. Cho, M. Matić, and J. Pečarić, Inequalities of Jensen’s type for Lipschitzian mappings, Comm. Appl. Nonlinear Anal. 8 (2001), no. 3, 37–46. · Zbl 0998.26015
[5] S. S. Dragomir, Inequalities of Lipschitz type for power series in Banach algebras, Ann. Math. Sil. 29 (2015), 61–83. · Zbl 1382.47003 · doi:10.1515/amsil-2015-0006
[6] S. S. Dragomir, Integral inequalities for Lipschitzian mappings between two Banach spaces and applications, Kodai Math. J. 39 (2016), no. 1, 227–251. · Zbl 1354.46018 · doi:10.2996/kmj/1458651701
[7] S. S. Dragomir and J. J. Koliha, Two mappings related to semi-inner products and their applications in geometry of normed linear spaces, Appl. Math. 45 (2000), no. 5, 337–355. · Zbl 0996.46007 · doi:10.1023/A:1022268627299
[8] J. L. W. V. Jensen, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Math. 30 (1906), no. 1, 175–193. · JFM 37.0422.02
[9] J. Mićić, J. Pečarić, and M. Praljak, Levinson’s inequality for Hilbert space operators, J. Math. Inequal. 9 (2015), no. 4, 1271–1285. · Zbl 1357.47018
[10] J. Pečarić, T. Furuta, J. Mićić Hot, and Y. Seo, Mond–Pečarić Method in Operator Inequalities, Monogr. Inequal. 1, Element, Zagreb, 2005. · Zbl 1135.47012
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