淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-0207200814085300
中文論文名稱 有關具對數型凹函數正數列的不等式
英文論文名稱 On inequalities of positive and logarithmically convex sequences
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 96
學期 2
出版年 97
研究生中文姓名 李嘉修
研究生英文姓名 Jia-shiou Li
學號 695190222
學位類別 碩士
語文別 中文
第二語文別 英文
口試日期 2008-05-30
論文頁數 38頁
口試委員 指導教授-楊國勝
委員-陳功宇
委員-曾貴麟
中文關鍵字 單調  不等式  幾何平均  比率  正序列  對數型凸函數  對數型凹函數  數學歸納法 
英文關鍵字 monotonicity  inequality  geometric meam  ratio  positive sequence  logarithmically concave  logarithmically convex  mathemathical induction 
學科別分類 學科別自然科學數學
中文摘要 在本文中我們推廣、整理了ㄧ些BAI-NI Gao 及 FENG QI所證明的不等式。
英文摘要 In the present note we established a generalization some of the inequalities that proof by BAI-NI Gao AND FENG QI.
論文目次 目 錄

1.簡介…………………………………………… P1.

2.主要結果……………………………………… P1.
定理1……………………………………………P1.
定理2……………………………………………P6.
定理3……………………………………………P10.

3.應用…………………………………………… P15.

4.參考文獻……………………………………… P17.

Contents

1.Introduction…………………………P20.

2.Main results.…………………………P20.
Theorem 1…………………………………P20.
Theorem 2…………………………………P25.
Theorem 3…………………………………P29.

3.Applications…………………………P34.

4.References……………………………P36.

參考文獻 [1] BAI-NI Gao AND FENG QI, Monotonicity of sequences involving geometric means of positive sequences with monotonicity and logarithmical convexity, Mathematicity Inequalities & Applications, 9, 1 (2006). 1-9.
[2] H. ALZER, On an inequality of H. Minc and L. Sathre, J. Math. Anal.Appl., 179, (1993), 396-402.
[3] B.-N. Guo, F. QI, Inequalities and monotonicity for the ratio of gamma functions, Taiwanese J. Math., 7, 2 (2003), 239-247.
[4] T. H. Chan, P. Gao and F. QI, On a generalization of Martins' inequality,Monatsh. Math., 138, 3 (2003), 179-187. RGMIA Res. Rep. Coll., 4, 1 (2001), Art.12, 93-101. Available online at URL: http://rgmia.vu.edu.au/v4n1.html.
[5] Chao-Ping Chen, Feng QI, P. Cerone and S.S. Dragomir, Monotonicity of Sequences Involving Convex and Concave Functions, Math. Inequal. Appl. 6, 2 (2003), 229-239. RGMIA Res. Rep. Coll., 5, 1 (2002), Art 1,3-13. Available online at URL: http://rgmia.vu.edu.au/v5n1.html.
[6] D. KERSHAW, A. LAFORGIA, Monotonicity results for the gamma function, Atti Accad. Sci. Torino Cl. SCI. Fis. Mat. Natur., 119, (1985),127-133.
[7] J.-CH. KUANG, Some extensions and refinements of Minc-Sathre inequality, Math. Gaz., 83, (1999), 123-127.
[8] H. MINC, L. SATHRE, Some inequalities involving (r!)^{(1/r)}, Proc. Edinburgh Math. Soc., 14, (1964/65), 41-46.
[9] J. PEČARIĆ, F. PROSCHAN, AND Y. L. TONG, Convex Functions, Partial Orderings, and Statistical Applications, Mathematics in Science and Engineering, 187, Academic Press, 1992.
[10] F. QI, An algebraic inequality, J. Inequal. Pure Appl. Math., 2, 1 (2001), Art. 13. Available online at URL: http://jipam .vu.edu.au/artical.php?sid=129. RGMIA Res Rep. Coll., 2, 1 (1999), Art. 8, 81-83. Available
online at URL: http://rgmia.vu.edu.au/v2n1.html.
[11] F. QI, Generalization of H. Alzer's inequality, J. Math. Anal. Appl.,240, (1999), 294-297.
[12] F. QI, Inequalities and monotonicity of sequences involving [n]√((n+k)!/k!),Soochow J. Math., 29, 4 (2004), 353-361. RGMIA Res. Rep. Coll., 2,5 (1999), Art. 8, 685-692. Available online at URL: http://rgmia.vu.edu.au/v2n5.html.
[13] F. QI, Inequalities and monotonicity of the ratio for the geometric means of a positive arithmetic sequence with unit difference, Internat. J. Math. Ed. Sci. Tech., 34, 4 (2003), 601-607. Austral. Math Soc. Gaz., 30, 3 (2003), 142-147. RGMIA Res. Rep. Coll., 6, (2003), suppl., Art. 2. Available online at URL: http://rgmia.vu.edu.au/v6(E).html
[14] B.-N. GUO, F. QI, Inequalities and monotonicity of the ratio for the geometric means of a positive arithmetic sequence with arbitrary difference, Tamkang. J. Math., 34, 3 (2003), 261-270.
[15] F. QI, On a new generalization of Martin's inequality, RGMIA Res. Rep. Coll., 5, 3 (2002), Art. 13, 527-578. Available online at URL: http://rgmia.vu.edu.au/v5n3.html.
[16] F. QI, B.-N. GUO, An inequality between ratio of the extended logarithmic means and ratio of the exponential means, Taiwanese J. Math., 7,2 (2003), 229-237. RGMIA Res. Rep. Coll., 4, 1 (2001), Art. 8, 55-61. Available online at URL: http://rgmia.vu.edu.au/v4n1.html.
[17] F. QI, B.-N. GUO, Monotonicity of sequences involving convex function and sequence, Math. Inequal. Appl. (2006), in press. RGMIA Res. Rep. Coll., 3, 2 (2000), Art. 14, 321-329. Available online at URL: http:// rgmia.vu.edu.au/v5n3.html.
[18] F. QI, B.-N. GUO, Monotonicity of sequences involving geometric means of postive sequences with logarithmical convexity, RGMIA Res. Rep. Coll., 5, 3 (2002), Art. 10, 497-507. Available online at URL: http:// rgmia.vu.edu.au/v3n2.html.
[19] F. QI, B.-N. GUO, Some inequalities involving the geometric mean of natural numbers and the ratio of gamma functions, RGMIA Res. Rep. Coll., 4, 1 (2001), Art. 6, 41-48. Available online at URL: http://rgmia.vu.edu.au/v4n1.html.
[20] F. QI, Q.-M. LUO, Generalization of H. Minc and J. Satnre's inequality, Tamkang J. Math., 31, 2 (2000), 145-148. RGMIA Res. Rep. Coll., 2, 6 (1999), Art. 14, 909-912. Available online at URL: http://rgmia.vu.edu.au/v2n6.html.
[21] F. QI, N. TOWGHI, Inequalities for the ratios of the mean values of functions, Nonlinear Funct. Anal. Appl., 9, 1 (2004), 15-23. An inequality for the ratios of the arithmetic means of functions with a positive parameter, RGMIA Res. Rep. Coll., 4, 2 (2001), Art. 15, 305- 309. Available online at URL:http://rgmia.vu.edu.au/v4n2.html.
[22] J. A. SAMPAIO MARTINS, Inequalities of Rado-Popoviciu type, In: Marques de Sá, Eduardo (ed.) et al. Mathematical studies. Homage to Professor Doctor Lús de Albuquerque. Coimbra: Universidade de Coimbra, Faculdade de Ciências e Tecnoligia, Departamento de Matemática, 169-175 (1994).
[23] J. SÁNDOR, On the gamma function, I-III, Publ. C. R. M. P. Neuchâtel,Série 1, 21, (1989), 4-7; Série 1, 28, (1997), 10-12; Série 2, 19 (2001), 33-40.
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2009-07-25公開。
  • 同意授權瀏覽/列印電子全文服務,於2009-07-25起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2281 或 來信