Abstract
The aim of this paper is to obtain a version of continuous functional calculus and some new envelope representation results in vector lattices as well as to indicate some applications.
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Kusraev A.G.: Functional calculus and Minkowski duality on vector lattices. Vladikavkaz. Math. J. 11(2), 31–42 (2009)
Kusraev, A.G.: Homogeneous Functional Calculus on Vector Lattices. Inst. Appl. Math. Inf. Vladikavkaz (2008)
Kusraev A.G.: Inequalities in vector lattices. In: Korobeĭnik, Yu.F., Kusraev, A.G. (eds) Studies on Mathematical Analysis, Differential Equations, and Their Applications, pp. 82–96. Southern Math. Inst., Vladikavkaz (2010)
Haase M.: Convexity inequalities for positive operators. Positivity. 11(1), 57–68 (2007)
Kutateladze S.S.: The Farkas lemma revisited. Siber. Math. J. 51(1), 78–87 (2010)
Aliprantis C.D., Burkinshaw O.: Positive Operators. Academic Press, London (1985)
Kusraev A.G.: Dominated Operators. Kluwer Academic Publ., Dordrecht (2000)
Meyer-Nieberg P.: Banach Lattices. Springer, Berlin (1991)
Kusraev A.G., Kutateladze S.S.: Subdifferentials: Theory and Applications. Kluwer Academic Publ., Dordrecht (1995)
Buskes G., de Pagter B., van Rooij A.: Functional calculus on Riesz spaces. Indag. Math. 4(2), 423–436 (1991)
Lozanovskiĭ G.Ya.: The functions of elements of vector lattices. Izv. Vyssh. Uchebn. Zaved. Mat. 4, 45–54 (1973)
Kutateladze S.S.: Fundamentals of functional analysis. Kluwer Academic Publ., Dordrecht (1996)
Rockafellar R.T.: Convex Analysis. Princeton Univ. Press, Princeton (1970)
Kutateladze S.S., Rubinov A.M.: Minkowski Duality and Its Applications. Nauka Publ., Novosibirsk (1976)
Pečarić J.E., Proschan F., Tong Y.L.: Convex Functions, Partial Orderings, and Statistical Application. Academic Press, Boston (1992)
Peetre, J., Persson, L.-E.: A general Beckenbach’s inequality with applications. In: Differential Operators and Nonlinear Analysis. Pitman Res. Notes Math., Ser. vol. 211, pp. 125–139 (1989)
Persson L.-E.: Generalizations of some classical inequalities and their applications. In: Krbec, M., Kufner, A., Opic, B., Rákosník, J. (eds) Nonlinear Analysis, Function Spaces and Applications, pp. 127–148. Teubner, Leipzig (1990)
Varošanec S.: A generalized Beckenbach–Dresher inequality. Banach J. Math. Anal. 4(1), 13–20 (2010)
Mitrinović D.S., Pečarić J.E., Fink A.M.: Classical and New Inequalities in Analysis. Kluwer Academic Publ., Dordrecht (1993)
Pečarić J.E., Beesack P.R.: On Jessen’s inequality for convex functions, II. J. Math. Anal. Appl. 118, 125–144 (1986)
Fiedler M. et al.: Linear Optimization Problems with Inexact Data. Springer, New York (2006)
Kutateladze S.S.: Boolean trends in linear inequalities. J. Appl. Ind. Math. 4(3), 340–348 (2010)
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In memory of Roko Aliprantis, a friend and a scholar.
Supported by a grant from Russian Foundation for Basic Research, project No. 09-01-00442.
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Kusraev, A.G., Kutateladze, S.S. Envelopes and inequalities in vector lattices. Positivity 15, 661–676 (2011). https://doi.org/10.1007/s11117-011-0134-8
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DOI: https://doi.org/10.1007/s11117-011-0134-8
Keywords
- Vector lattice
- Functional calculus
- Envelope representation
- Convexity inequality
- Sublinear operator
- Superlinear operator
- Polyhedral operator
- Interval operator
- Interval analysis
- Subdifferential