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論文名稱 The P-class and Q-class functions on symmetric cones
發表日期 2020-08-01
論文收錄分類 SCI
所有作者 CHIEN-HAO HUANG、YU-LIN CHANG、JEIN-SHAN CHEN
作者順序 第一作者
通訊作者
刊物名稱 Journal of Nonlinear and Variational Analysis
發表卷數 4
是否具有審稿制度
發表期數 2
期刊或學報出版地國別/地區 NATCAN-加拿大
發表年份 2020
發表月份 8
發表形式 電子期刊
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[英文摘要] :
In this paper, we investigate the functions of P-class and of Q-class associated with symmetric cones. We provide the characterizations for P-class functions on symmetric cones, and discuss the relationship between P-class functions and monotone functions in the setting of symmetric cones. In addition, we also discuss the sufficient conditions for Q-class functions being monotone in the setting of symmetric cones.

[參考文獻] :
[1] M. Bakherad, H. Abbas, B. Mourad, M.S. Moslehian, Operator P-class functions, J. Inequal. Appl. 2014 (2014), 451 .
[2] H.H. Bauschke, M. Koecher, Jordan-Algebren, Springer, New York, 1966.
[3] Y.-L. Chang, J-S. Chen, Convexity of symmetric cone trace functions in Euclidean Jordan algebras, J. Nonlinear Convex Anal. 14 (2013), 53-61 .
[4] Y.-L. Chang, J-S. Chen, S. Pan, Symmetric cone monotone functions and Symmetric cone convex functions, J. Nonlinear Convex Anal. 17(3) (2016), 499-512.
[5] J.-S. Chen, The convex and monotone functions associated with second-order cone, Optimization 55 (2006), 363-385.
[6] J.-S. Chen, X. Chen, S.-H. Pan, J.-W. Zhang, Some Characterizations of SOC-monotone and SOC-convex functions, J. Global Optim. 45 (2009), 259-279.
[7] S. S. Dragomir, J. Pecaric, L.E. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21 (1995), 335-341.
[8] S.S. Dragomir, C.E.M. Pearce, On Jensen’s inequality for a class of functions of Godunova and Levin, Period. Math. Hung. 33 (1996), 93-100.
[9] S.S. Dragomir, C.E.M. Pearce, Quasi-convex functions and Hadamard’s inequality, Bull. Aust. Math. Soc. 57 (1998), 377-385.
[10] J.I. Fujii, M. Kian, M.S. Moslehian, Operator Q-class functions, Sci. Math. Jpn. 73 (2010), 75-80.
[11] M. Fukushima, Z.-Q. Luo, P. Tseng, Smoothing functions for second-order-cone complimentarity problems, SIAM J. Optim. 12 (2002), 436-460.
[12] J. Faraut, A. Kor´anyi, Analysis on Symmetric Cones, Oxford Mathematical Monographs Oxford University Press, New York, 1994.
[13] E.K. Godunova, V.I. Levin, Inequalities for functions of a broad class that contains convex, monotone and some other forms of functions, (Russian) Numerical mathematics and mathematical physics (Russian), vol. 166, pp. 138–142, Moskov. Gos. Ped. Inst., Moscow, 1985.
[14] M. Koecher, The Minnesota Notes on Jordan Algebras and Their Applications, edited and annotated by A. Brieg and S. Walcher, Springer, Berlin, 1999.
[15] S.-H. Pan, Y. Chiang, J.-S. Chen, SOC-monotone and SOC-convex functions v.s. matrix monotone and matrix convex functions, Linear Algebra Appl. 437 (2012), 1264-1284.
[16] C.E.M. Pearce, P-functions, quasi-convex functions, and Hadamard-type inequalities, J. Math. Anal. Appl. 240 (1999), 92-104.
[17] M. Radulescu, S. Radulescu, P. Alexandrescu, On Schur inequality and Schur functions, Ann. Univ. Craiova, Mathematics and Computer Science Series, 32 (2005), 202-208.
[18] M. Radulescu, S. Radulescu, P. Alexandrescu, On the Godunova–Levin–Schur class of functions, Math. Inequal. Appl. 12 (2009), 853-862.
[19] J. Rooin, S. Habibzadeh, M.S. Moslehian, Jensen inequalities for P-class functions, Period. Math. Hung. 77 (2017), 1-13.
[20] M.Z. Sarikaya, E. Set, M.E. Ozdemir, On some new inequalities of Hadamard type involving h-convex functions, Acta Math. Univ. Comen. 2 (2010), 265-272.
[21] D. Sun, J. Sun, L¨owner’s operator and spectral functions in Euclidean Jordan algebras, Math. Oper. Res. 33 (2008), 421-445.
[22] J. Tao, M.S. Gowda, Some P-properties for nonlinear transformations on Euclidean Jordan algebras, Math. Oper. Res. 30 (2005), 985-1004.