Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (4): 698-708.
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CHU Yu-Ming1, ZHANG Xiao-Ming2, SHI Huan-Nan3
Received:
2010-09-11
Revised:
2011-11-15
Online:
2012-08-25
Published:
2012-08-25
Supported by:
国家自然科学基金(11071069, 11171307)和湖南省自然科学基金(09JJ6003)资助
CLC Number:
CHU Yu-Ming, ZHANG Xiao-Ming, SHI Huan-Nan. Gautschi-type Inequalities and Their Applications[J].Acta mathematica scientia,Series A, 2012, 32(4): 698-708.
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[1] Whittaker E T, Watson G N. A Course of Modern Analysis. New York: Cambridge Univ press, 1962 [2] 赵如汉. 加权Bergman 空间中函数的几个严格不等式. 数学物理学报, 2010, 30A(5): 1306--1312 [3] 刘晓鹏, 刘坤会. F分布密度曲线之变化. 数学物理学报, 2007, 27A(2): 331--342 [4] Lu S C, Ni G J. The application of homogeneous function analysis to relativistic WKB approximations. Acta Math Sci, 1992, 12(1): 71--78 [5] Chu Y M, Zhang X M, Zhang Z H. The geometric convexity of a function involving gamma function with applications. Commun Korean [6] Zhang X M, Chu Y M, Zhang X H. The Hermite-Hadamard type inequality of GA-convex functions and its applications. J Inequal Appl, 2010, Article ID 507560, 11 pages [7] Zhang X M, Chu Y M. A double inequality for gamma function. J Inequal Appl, 2009, Article ID 503782, 7 pages [8] Zhao T H, Chu Y M, Jiang Y P. Monotonic and logarithmically convex properties of a function involving gamma functions. J Inequal Appl, 2009, Article ID 728612, 13 pages [9] Chu Y M, Zhang X M, Tang X M. An elementary inequality for psi function. Bull Inst Math Acad Sin, 2008, 3(3): 373--380 [10] Zhang X M, Chu Y M. An inequality involving the gamma function and the psi function. Int J Mod Math, 2008, 3(1): 67--73 [11] Zhao T H, Chu Y M, A class of logarithmically completely monotonic functions associated with a gamma function. J Inequal Appl, 2010, Article ID 392431, 11 pages [12] Kumar P, Singh S P, Dragomir S S. Some inequalities involving beta and gamma functions. Nonlinear Anal Forum, 2001, 6(1): 143--150 [13] Berg C, Pedersen H L. Pick functions related to the gamma function. Rocky Mountain J Math, 2002, 32(2): 507--525 [14] Alzer H. On Ramanujan's double inequality for the gamma function. Bull London Math Soc, 2003, 35(5): 601--607 [15] Chen C P, Qi F. Logarithmically completely monotonic functions relating to the gamma function. J Math Anal Appl, 2006, 321(1): 405--411 [16] Alzer H, Grinshpan A Z. Inequalities for the gamma and q-gamma functions. J Approx Theory, 2007, 144(1): 67--83 [17] Laforgia A. Further inequalities for the gamma function. Math Comp, 1984, 42(166): 597--600 [18] Lorch L. Comparsion of a pair of upper bounds for a ratio of gamma functions. Math Balkanica, 2002, 16(1--4): 195--202 [19] Natalini P, Palumbo B. Some monotonicity results on the zeros of the generalized Laguerre ploynomials, J Comput Appl Math, [20] Lv Y P, Sun T C, Chu Y M. Necessary and sufficient conditions for a class of functions and their reciprocals to be logarithmically completely monotonic. Journal of Inequalities and Applications, 2011, 2011: 36 [21] Clark W E, Ismail M E H. Binomial and Q-binomial coefficient inequalities related to the hamiltonicity of the Kneser graphs and their Q-analogues. J Combin Theory (Ser A), 1996, 76(1): 83--98 [22] Grabner P J, Tichy R F, Zimmermann U T. Inequalities for the gamma function with applications to permanents. Discrete Math, [23] Gautschi W. Some elementary inequalities relating to the gamma and incomplete gamma function. J Math and Phys, 1959/1960, [24] Erber T. The gamma function inequalities of gurland and gautschi. Skand Aktuarietidskr, 1961, 1960: 27--28 [25] Ke\v{c}ki\'{c} J D, Vasi\'{c} P M. Some inequalities for the gamma function. Publ Inst Math, 1971, 11(25): 107--114 [26] Kershaw D. Some extensions of W. Gautschi's inequalities for the gamma function. Math Comp, 1983, 41(164): 607--611 [27] Mitrinovi\'{c} D S, Pe\v{c}ari\'{c} J E, Fink A M. Classical and New Inequalities in Analysis. Dordrecht: Kluwer Academic Publishers Group, 1993 [28] Elbert Á, Laforgia A. On some properties of the gamma function. Proc Amer Math Soc, 2000, 128(9): 2667--2673 [29] Fichtenholz G M. Differential-und Integralrechnung II. Berlin: VEB Deutscher Verlag der Wissenschaften, 1964 [30] Sándor J, Debnath L. On certain inequalities involving the constant e and their applications. J Math Anal Appl, 2000, 249(2): 569--582 [31] Chu Y M, Wang S S, Zong C. Optimal lower power mean bound for the convex combination of harmonic and logarithmic means. [32] Chu Y M, Xia W F. Two optimal double inequalities between power mean and logarithmic mean. Comput Math Appl, 2010, 60(1): 83--89 [33] Chu Y M, Long B Y. Best possible inequalities between generalized logarithmic mean and classical means. Abstr Appl Anal, 2010, Article ID 303286, 13 pages [34] Wang M K, Qiu Y F, Chu Y M. Sharp bounds for Seiffert means in terms of Lehmer means. J Math Inequal, 2010, 4(4): 581--586 [35] Long B Y, Chu Y M. Optimal inequalities for generalized logarithmic, arithmetic, and geometric means. J Inequal Appl, 2010, Aricle ID 806825, 10 pages [36] Chu Y M, Xia W F. Inequalities for generalized logarithmic means. J Inequal Appl, 2009, Article ID 763252, 7 pages [37] Wang M K, Chu Y M, Qiu Y F. Some comparison inequalities for generalized muirhead and identric means. J Inequal Appl, 2010, [38] Shi M Y, Chu Y M, Jiang Y P. Optimal inequalities among various means of two arguments. Abstr Appl Anal, 2009, Article ID 694394, 10 pages [39] Qiu Y F, Wang M K, Chu Y M, Wang G D. Two sharp inequalities for Lehmer mean, identirc mean and logarithmic mean. J Math Inequal, 2011, 5(3): 301--306 [40] Chu Y M, Wang M K, Qiu Y F. An optimal double inequality between power-type Heron and Seiffert means. J Inequal Appl, 2010, [41] Chu Y M, Qiu Y F, Wang M K. Sharp power mean bounds for the combination of Seiffert and geometric means. Abstr Appl Anal, [42] Chu Y M, Qiu Y F, Wang M K, Wang G D. The optimal convex combination bounds of arithmetic and harmonic means for the Seiffert's mean. J Inequal Appl, 2010, Article ID 436457, 7 pages |
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