Weighted Jessen's functionals and exponential convexity
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Authors
Rishi Naeem
- School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan.
Matloob Anwar
- School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan.
Abstract
In this paper, we give a refinement of the well known Jessen's
inequality via weight functions. We discuss \(m\)-exponential
convexity of the functions associated with these weighted Jessen's
functionals. Cauchy and Lagrange mean value theorems are also given
that are useful in the construction of means with Stolarsky
property.
Share and Cite
ISRP Style
Rishi Naeem, Matloob Anwar, Weighted Jessen's functionals and exponential convexity, Journal of Mathematics and Computer Science, 19 (2019), no. 3, 171--180
AMA Style
Naeem Rishi, Anwar Matloob, Weighted Jessen's functionals and exponential convexity. J Math Comput SCI-JM. (2019); 19(3):171--180
Chicago/Turabian Style
Naeem, Rishi, Anwar, Matloob. "Weighted Jessen's functionals and exponential convexity." Journal of Mathematics and Computer Science, 19, no. 3 (2019): 171--180
Keywords
- Convex function
- Jessen's inequality
- log-convex functions
- exponentially convex function
- mean value theorems
- Stolarsky means
MSC
References
-
[1]
M. Anwar, N. Latif, J. Pečarić, Positive semidefinite matrices, exponential convexity for majorization, and related Cauchy means, J. Inequal. Appl., 2010 (2010), 19 pages
-
[2]
S. I. Butt, R. Jakšić, L. Kvesić, J. Pečarić, $n$--Exponential convexity of weighted Hermite--Hadamard's inequality, J. Math. Inequal., 8 (2014), 299--311
-
[3]
S. S. Dragomir, J. Pečarić, L. E. Persson, Properties of some functionals related to Jensen's inequality, Acta Math. Hungar., 70 (1996), 129--143
-
[4]
S. Iqbal, K. Krulić Himmelreich, J. Pečarić, D. Pokaz, $n$--Exponential convexity of Hardy--type and Boas--type functionals, J. Math. Inequal., 7 (2013), 739--750
-
[5]
J. Jakšetić, R. Naeem, J. Pečarić, Exponential convexity for Jensen's inequality for norms, J. Inequal. Appl., 2016 (2016), 8 pages
-
[6]
J. Jakšetić, J. Pečarić, Exponential Convexity method, J. Convex Anal., 20 (2013), 181--197
-
[7]
B. Jessen, Bemaerkinger om konvekse Funktioner og Uligheder imellem Middelvaerdier I, Mat. Tidsskrift B, 1931 (1931), 17--28
-
[8]
S. Khalid, J. Pečarić, On the refinements of the integral Jensen--Steffensen inequality, J. Inequal. Appl., 2013 (2013), 18 pages
-
[9]
K. A. Khan, A. Nosheen, J. Pečarić, $n$--Exponential convexity of some dynamic Hardy--type functionals, J. Math. Inequal., 8 (2014), 331--347
-
[10]
A. R. Khan, J. Pečarić, M. Rodić Lipanović, $n$--Exponential convexity for Jensen--type inequalities, J. Math. Inequal., 7 (2013), 313--335
-
[11]
D. S. Mitrinović, J. E. Pečarić, A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers Group, Dordrecht (1993)
-
[12]
R. Naeem, $m$--Exponential convexity of refinements of Hermite--Hadamards inequality, Proc. Pak. Acad. Sci. A, 54 (2017), 197--205
-
[13]
R. Naeem, M. Anwar, Jessen type functionals and exponential convexity, J. Math. Computer Sci., 17 (2017), 429--436
-
[14]
J. Pečarić, J. Perić, Improvements of the Giaccardi and the Petrović inequality and related Stolarsky type means, An. Univ. Craiova Ser. Mat. Inform., 39 (2012), 65--75
-
[15]
J. E. Pečarić, F. Proschan, Y. L. Tong, Convex functions, partial orderings, and statistical applications, Academic Press, Boston (1992)
-
[16]
J. Rooin, A refinement of Jensen's inequality, J. Inequal. Pure Appl. Math., 6 (2005), 4 pages
-
[17]
J. Rooin, Some refinements of discrete Jensen's inequality and some of its applications, Nonlinear Funct. Anal. Appl., 12 (2007), 107--118
-
[18]
W. Rudin, Real and complex analysis, McGraw-Hill Book Co., New York (1966)
