Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T17:17:20.617Z Has data issue: false hasContentIssue false
  • English
  • Français

A CONCEPT OF SYNCHRONICITY ASSOCIATED WITH CONVEX FUNCTIONS IN LINEAR SPACES AND APPLICATIONS

Part of: Inequalities

Published online by Cambridge University Press:  18 June 2010

S. S. DRAGOMIR
S. S. DRAGOMIR*
Affiliation:
Mathematics, School of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, Vic 8001, Australia School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag-3, Wits-2050, Johannesburg, South Africa (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A concept of synchronicity associated with convex functions in linear spaces and a Chebyshev type inequality are given. Applications for norms, semi-inner products and convex functions of several real variables are also given.

Keywords

convex functionsGâteaux derivativesnormssemi-inner productssynchronous sequencesChebyshev inequality

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 2 , October 2010 , pp. 328 - 339
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Ansari, A. H. and Moslehian, M. S., ‘More on reverse triangle inequality in inner product spaces’, Int. J. Math. Math. Sci. 2005(18) (2005), 2883–2893.CrossRefGoogle Scholar
[2]Ansari, A. H. and Moslehian, M. S., ‘Refinements of reverse triangle inequalities in inner product spaces’, J. Inequal. Pure Appl. Math. 6(3) (2005), Article 64, 12 pp (electronic).Google Scholar
[3]Brnetić, I., Dragomir, S. S., Hoxha, R. and Pečarić, J., ‘A reverse of the triangle inequality in inner product spaces and applications for polynomials’, Aust. J. Math. Anal. Appl. 3(2) (2006), Art. 9,8 pp.Google Scholar
[4]Cho, Y. J., Matić, M. and Pečarić, J., ‘Inequalities of Hlawka’s type in n-inner product spaces’, Commun. Korean Math. Soc. 17(4) (2002), 583–592.CrossRefGoogle Scholar
[5]Dragomir, S. S., ‘An improvement of Jensen’s inequality’, Bull. Math. Soc. Sci. Math. Roumanie 34(82)(4) (1990), 291–296.Google Scholar
[6]Dragomir, S. S., ‘Some refinements of Ky Fan’s inequality’, J. Math. Anal. Appl. 163(2) (1992), 317–321.CrossRefGoogle Scholar
[7]Dragomir, S. S., ‘Some refinements of Jensen’s inequality’, J. Math. Anal. Appl. 168(2) (1992), 518–522.CrossRefGoogle Scholar
[8]Dragomir, S. S., ‘A further improvement of Jensen’s inequality’, Tamkang J. Math. 25(1) (1994), 29–36.CrossRefGoogle Scholar
[9]Dragomir, S. S., ‘A new improvement of Jensen’s inequality’, Indian J. Pure Appl. Math. 26(10) (1995), 959–968.Google Scholar
[10]Dragomir, S. S., Semi-inner Products and Applications (Nova Science Publishers, New York, 2004).Google Scholar
[11]Dragomir, S. S., ‘A new refinement of Jensen’s inequality in linear spaces with applications’, RGMIA Res. Rep. Coll. 12 (2009), Preprint, Supplement, Article 6. http://www.staff.vu.edu.au/RGMIA/v12(E).asp.Google Scholar
[12]Dragomir, S. S., ‘Inequalities in terms of the Gâteaux derivatives for convex functions in linear spaces with applications’, RGMIA Res. Rep. Coll. 12 (2009), Preprint, Supplement, Article 7. http://www.staff.vu.edu.au/RGMIA/v12(E).asp.Google Scholar
[13]Dragomir, S. S., ‘A refinement of Jensen’s inequality with applications for f-divergence measures’, Taiwanese J. Math. 14(1) (2010), 153–164.CrossRefGoogle Scholar
[14]Dragomir, S. S. and Goh, C. J., ‘A counterpart of Jensen’s discrete inequality for differentiable convex mappings and applications in information theory’, Math. Comput. Modelling 24(2) (1996), 1–11.CrossRefGoogle Scholar
[15]Dragomir, S. S. and Ionescu, N. M., ‘Some converse of Jensen’s inequality and applications’, Rev. Anal. Numér. Théor. Approx. 23(1) (1994), 71–78.Google Scholar
[16]Dragomir, S. S., Pečarić, J. and Persson, L. E., ‘Properties of some functionals related to Jensen’s inequality’, Acta Math. Hungar. 70(1–2) (1996), 129–143.CrossRefGoogle Scholar
[17]Dragomir, S. S., Pečarić, J. and Sándor, J., ‘The Chebyshev inequality in pre-Hilbertian spaces. II’, Proceedings of the Third Symposium of Mathematics and its Applications (Timişoara, 1989) (Romanian Acad., Timişoara, 1990), pp. 75–78.Google Scholar
[18]Dragomir, S. S. and Sándor, J., ‘The Chebyshev inequality in pre-Hilbertian spaces. I’, Proceedings of the Second Symposium of Mathematics and its Applications (Timişoara, 1987) (Romanian Acad., Timişoara, 1988), pp. 61–64.Google Scholar
[19]Miličić, P. M., ‘Sur le semi-produit scalaire dans quelques espaces vectorial normés’, Mat. Vesnik 8(23) (1971), 181–185.Google Scholar
[20]Miličić, P. M., ‘Sur une inégalité complémentaire de l’inégalité triangulaire’, Mat. Vesnik 41(2) (1989), 83–88.Google Scholar
[21]Pečarić, J. and Dragomir, S. S., ‘A refinements of Jensen inequality and applications’, Stud. Univ. Babeş-Bolyai, Math. 24(1) (1989), 15–19.Google Scholar
[22]Pečarić, J. and Rajić, R., ‘The Dunkl–Williams inequality with n elements in normed linear spaces’, Math. Inequal. Appl. 10(2) (2007), 461–470.Google Scholar