n-EXPONENTIAL CONVEXITY FOR JENSEN-TYPE INEQUALITIES

被引：20
作者：
Khan, Asif R. [1 ,2 ]
Pecaric, Josip [2 ,3 ]
Lipanovic, Mirna Rodic [3 ]
机构：
[1] Univ Karachi, Dept Math Sci, Karachi, Pakistan
[2] Govt Coll Univ, Abdus Salam Sch Math Sci, Lahore, Pakistan
[3] Univ Zagreb, Fac Textile Technol, Zagreb 10000, Croatia
来源：
JOURNAL OF MATHEMATICAL INEQUALITIES | 2013年 / 7卷 / 03期
关键词：
Green function; Jensen inequality; converse of the Jensen inequality; Cauchy-type mean value theorems; n-exponential convexity; exponential convexity; log-convexity; means;
D O I：
10.7153/jmi-07-29
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Starting from the results given in [14] where the uniform treatment of the Jensen type inequalities and its converses is given, we investigate the exponential convexity of differences of the left-hand and the right-hand side of these inequalities. Using these differences, we produce new exponentially convex functions. Finally, we give several examples of the families of functions for which the obtained results can be applied, and we get some generalized Cauchy means. Results from this paper present the generalization of the results from [2].
引用
收藏
页码：313 / 335
页数：23
相关论文
共 16 条
  • [1] [Anonymous], MEANS THEIR INEQUALI
  • [2] [Anonymous], 1992, Math. Sci. Eng
  • [3] Anwar M, 2011, B MALAYS MATH SCI SO, V34, P31
  • [4] EXPONENTIAL CONVEXITY, POSITIVE SEMI-DEFINITE MATRICES AND FUNDAMENTAL INEQUALITIES
    Anwar, M.
    Jaksetic, J.
    Pecaric, J.
    Rehman, Atiq Ur
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2010, 4 (02): : 171 - 189
  • [5] EXTENSIONS OF THE HERMITE-HADAMARD INEQUALITY WITH APPLICATIONS
    Bakula, M. Klaricic
    Pecaric, J.
    Peric, J.
    [J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2012, 15 (04): : 899 - 921
  • [6] Boas RP., 1970, Publ. Elektroteh. Fak. Univ. Beogr. Ser. Mat, V302, P1
  • [7] Brunk H., 1956, P AM MATH SOC, V7, P817, DOI 10.1090/S0002-9939-1956-0081371-9
  • [8] JAKSETIC J., J CONVEX AN IN PRESS
  • [9] Some new inequalities involving elementary mean values
    Mercer, AM
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 229 (02) : 677 - 681
  • [10] An "error term" for the Ky Fan inequality
    Mercer, AM
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 220 (02) : 774 - 777
12