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        關(guān)于Kadison算子型不等式的推廣及其經(jīng)濟應用

        發(fā)布時(shí)間:2024-11-13 12:34:47   來(lái)源:作文大全    點(diǎn)擊:   
        字號:

        工作及本文研究提供了方法. T.Furuta(2011 [7]利用Furuta不等式推廣J.C. Bourin與E. Ricard的工作. 原江濤(2012)[8]進(jìn)一步改進(jìn)T. Furuta 的工作, 并給出更加精細的估計. 本文正是借鑒以上工作, 得到了一些新的結果, 并利用共軛算子及凸性算子的性質(zhì)給出兩種經(jīng)濟模型的解釋.

        2 預備知識

        參考文獻

        [1] M FUJII, Y O KIM, R NAKAMOTO. A characterization of convex functions and its application to operator monotone functions[J].Banach Journal of Mathematical Analysis,2014,8(2): 118-123.

        [2] 劉衛鋒. 三參數區間數集成算子及決策應用[J].經(jīng)濟數學(xué),2014,31(4):96-101.

        [3] T ANDO. Concavity of certain maps on positive definite matrices and applications to hadamard products[J]. Linear Algebra and its Applications, 1979, 26(4):203-241.

        [4] L ZHOU, H CHEN, J LIU. Generalized multiple averaging operators and their applications to group decision making[J]. Group Decision and Negotiation, 2013, 22(2): 331-358.

        [5] R. KADISON. A generalized Schwarz inequality and algebraic invariants for operator algebras[J]. Annals of Mathematics, 1952, 56(3):494-503.

        [6] J BOURIN, E RICHARD. An asymmetric Kadison’s inequality[J]. Linear Algebra and its Applications, 2010, 433(3):499-510.

        [7] T FURUTA. Around choi inequalities for positive linear maps[J]. Linear Algebra and its Applications, 2011, 434(1):14-17.

        [8] J YUAN, G JI. Extensions of Kadison’s inequality on positive linear maps[J]. Linear Algebra and its Applications, 2012, 436(3):747-752.

        [9] M CHOI. Some assorted inequalities for positive linear map onCalgebras[J]. Journal of Operator Theory, 1980, 4(2):271-285.

        [10]R BHATIA. Positive Definite Matrices[M]. Princeton: Princeton University Press, 2007.

        [11]F HENSEN, J PECARIC, I. PERIC. Jensen’s operator inequality and its converses[J]. Mathematica Scandinavica, 2007, 100(1):61-73.

        [12]G PEDERSEN. Some operator monotone functions[J]. Proceedings of the Americal Mathematical Society, 1972, 36(1):309-310.

        [13]T FURUTA.A≥B≥0assures(BrApBr)1q≥Bp+2rqforr≥0,p≥0,q≥1With(1+2r)q≥p+2r[J]. Proceedings of the Americal Mathematical Society, 1987, 101(1):85-88.

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