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QUASILINEARITY OF SOME COMPOSITE FUNCTIONALS WITH APPLICATIONS

  • S. S. DRAGOMIR (a1) (a2)

Abstract

The quasilinearity of certain composite functionals defined on convex cones in linear spaces is investigated. Applications in refining the Jensen, Hölder, Minkowski and Schwarz inequalities are given.

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References

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[1]Alzer, H., ‘Sub- and superadditive properties of Euler’s gamma function’, Proc. Amer. Math. Soc. 135(11) (2007), 36413648.
[2]Dragomir, S. S., Advances in Inequalities of the Schwarz, Triangle and Heisenberg Type in Inner Product Spaces (Nova Science Publishers, New York, 2007).
[3]Dragomir, S. S., ‘Inequalities for superadditive functionals with applications’, Bull. Aust. Math. Soc. 77 (2008), 401411.
[4]Dragomir, S. S. and Mond, B., ‘On the superadditivity and monotonicity of Schwarz’s inequality in inner product spaces’, Contributions, Macedonian Acad. Sci. Arts 15(2) (1994), 522.
[5]Dragomir, S. S., Pečarić, J. and Persson, L. E., ‘Properties of some functionals related to Jensen’s inequality’, Acta Math. Hungar. 70 (1996), 129143.
[6]Losonczi, L., ‘Sub- and superadditive integral means’, J. Math. Anal. Appl. 307(2) (2005), 444454.
[7]Trimble, S. Y., Wells, J. and Wright, F. T., ‘Superadditive functions and a statistical application’, SIAM J. Math. Anal. 20(5) (1989), 12551259.
[8]Vitolo, A. and Zannier, U., ‘Inequalities for superadditive functions related to a property R [of] convex sets’, Boll. Unione Mat. Ital. A (7) 4(3) (1990), 309314.
[9]Volkmann, P., ‘Sur les fonctions simultanément suradditives et surmultiplicatives’, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 28(76)(2) (1984), 181184.
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QUASILINEARITY OF SOME COMPOSITE FUNCTIONALS WITH APPLICATIONS

  • S. S. DRAGOMIR (a1) (a2)

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